What was going on when I was born?

The stock market extended its gains yesterday for a second session in a broader-based upswing. The rally, which came on active trading, was paced by further improvement in the credit markets and gains among the airline stocks. On the New York Stock Exchange, the Dow Jones industrial average closed up 10.60 points, to 1,107.55. In the last two days, the Dow has gained 21 points. It had closed at a 17-month low Tuesday.

The Continental Rescue The Government announced a $4.5 billion package of support for Continental Illinois, in an extraordinary intervention into the banking business. The plan, which includes $1 billion of fresh capital, gives effective control of the bank to the Government, which also assumes $3.5 billion in delinquent loans. (Page A1.) The move shows that Washington is willing to accept responsibility for the success of individual enterprises, as well as the economy in general. (A1.) Named to breathe life into the bank were John Swearingen, former chairman of Standard Oil of Indiana, and William Ogden, former vice chairman of Chase Manhattan. (D17.) The rescue package could make Continental prosperous, analysts said. But in Washington questions were raised about the scope of banking regulations. (D17.)

The Federal Communications Commission, seeking to further encourage media competition, voted yesterday to increase the number of commercial television stations that an individual or company may own. The increase, to 12 stations from 7, and a decision to remove nearly all restrictions on ownership of broadcast outlets in 1990 repealed a 31-year-old rule. The commission's actions, taken by a 4-to-1 vote, will also allow ownership of up to 12 AM and 12 FM radio stations until the restrictions end in 1990. Individuals and companies had previously been limited to owning seven of each.

The decision to save the Continental Illinois National Bank and Trust Company appears to prove once again that Washington has accepted far-reaching responsibility not only for the success of the economy, but also for individual enterprises - if they are big enough. At the same time, the rescue appeared to strengthen the hand of Congressional Democrats, and a few Republicans, who argue that banks are profoundly different from other lines of business - essentially because of their importance as a source of funds for business - and that they require tighter restraints and supervision than other companies. On its face, the $4.5 billion rescue of the big Chicago bank departs significantly from the preference for market discipline - the sink or swim philosophy - that the Administration has proclaimed as the linchpin of its economic policy and its effort to deregulate business and industry. The banking agencies agreed to provide help for one reason: ''to avoid general instability in the financial system,'' as the official announcement said. The fear was that Continental's failure would set off financial chaos. That fear has been voiced by Government officials - from the Federal Reserve System, the Office of the Comptroller of the Currency and the Federal Deposit Insurance Corporation, in public declarations and private comments - ever since the shoring-up of Continental in May.

''I got my house, I got my tomatoes, I got whatever I need.

President Fidel Castro said tonight that he would welcome any steps to lessen bitter tensions between the United States and Cuba. In a speech marking the 31st anniversary of the Cuban revolution, Mr. Castro praised the Rev. Jesse Jackson as a man of peace and, in a conciliatory gesture, said he would seriously consider ''any efforts at decreasing tensions in our area and in the rest of the world, any efforts aimed at decreasing the dangers of the madness of war.'' Mr. Castro's remarks were in sharp contrast to the vitriolic name-calling of his anniversary speech last year. The senior United States diplomat in Cuba walked out of that speech in protest. Mr. Castro noted tonight that the socialist system in his country and the capitalist system in the United States were ''totally different,'' but he suggested that ''peaceful coexistence'' was possible.

Music can't help changing when it hits the open air. Sprung from the confines of clubs and theaters, it floats in all directions, battling ambient noises and transforming activities wherever it carries. In earlier days, outdoor concerts called for specially designed music - loud, rousing stuff with a heritage that stretches from Handel's ''Royal Fireworks Music'' to Tchaikovsky's ''1812'' Overture and Messiaen's ''Et Exspecto Resurrectionem Mortuorum.'' The amplifier changed that, but not completely; the outdoors are still no place for subtlety or brooding. With a celebratory tune and a high-powered beat, however, an outdoor concert can make the whole city seem to be rocking in rhythm. While the best-known outdoor concert this weekend is probably the sold-out Jacksons' tour stop at Giants Stadium, it's not the only show on the docket. There are jazz-rock and pop-jazz at Pier 84 this weekend; Latin jazz tonight at the South Street Seaport's Summerpier; 1960's pop at Jones Beach, and outdoor jazz concerts scattered all around the city and Long Island.

The consequences of the ''equal access'' bill may dismay supporters who thought it would put prayer back in schools. News analysis, page B11. WASHINGTON, July 26 - As political maneuvering accelerated on Capitol Hill today, the House of Representatives defeated a proposal by conservative Republicans that would have punished localities forbidding voluntary prayer in public schools. In the key vote, the proposal lost 215 to 194. Only 33 Republicans joined 182 Democrats in opposing the measure, and the sponsors said they had scored a political triumph by forcing so many Democrats to cast a vote that might prove unpopular back home.

The Long Island Lighting Company has had to defer some repair work but has performed well in maintaining service since a strike that began July 10, the State Public Service Commission said today. However, Lilco probably will need outside contractors to hook up new customers and perform major maintenance work if the strike continues much longer, according to the commission, which is monitoring the company's performance. ''With the storms that they've had, the restoration of service has been good,'' said Edward J. Murphy, who heads the seven-member monitoring group. He said that the 1,475 management personnel who are filling in for 3,900 striking members of the International Brotherhood of Electrical Workers had restored electric service to customers after storms in ''comparable time to what they would have done with the union.'' Lilco serves 900,000 customers in Nassau and Suffolk Counties and the Rockaway peninsula of Queens.

In New York State, there is ''The Tempest'' by an Italian theater company and Eugene O'Neill in dance and jazz. In Connecticut, there is a new Australian play staged by Australian actors, an Argentine play presented by Argentines and such familiar old American tunes as ''Button Up Your Overcoat'' in a musical revival. In Massachusetts, the fare ranges from Chekhov in Williamstown and Shakespeare in Lenox to the first play by a woman to win the Pulitzer Prize for drama, which is now on the boards in Stockbridge but may be New York- bound. Such is the range of summer theater in the region this weekend. The season is in full swing, and a tour of the straw-hat trail includes the following offerings: Tonight and tomorrow night at 8, Pepsico Summerfare '84, in Purchase, N.Y., presents ''La Tempesta,'' an Italian version of Shakesepare's ''Tempest'' by the Piccolo Teatro di Milano.

The Leucadia National Corporation, an insurance and consumer lending company, offered yesterday to pay $930 million in cash for the 88 percent of the Avco Corporation that it does not yet own. Robert P. Bauman, 52-year-old chairman and chief executive of Avco, a big military supplier with major interests in insurance and consumer lending, immediately assailed the offer as ''entirely unacceptable.'' He said he felt shareholders would best be served if the company remained independent. Directors are expected to reject the offer at a regular board meeting today.

When seven regional telephone companies were about to be broken away from Ma Bell, many investment handicappers predicted that Ameritech, the Chicago-based regional, would bring up the rear in the race of the new Seven Sisters. Wall Street's handicappers cited two reasons for their dour predictions about Ameritech: it is situated in one of the nation's slowest-growing regions in terms of population, and its service area includes the Middle West's Rust Belt and its array of declining industries. But once the regionals went into business last Jan. 1, Ameritech surprised everyone by sprinting out in front of its sister companies. In its first two quarters, Ameritech's return on equity was the highest of the regionals. It was the first regional to market cellular mobile telephones, and, many industry analysts say, it has achieved the lowest cost per telephone line.