The stock market tumbled today to its lowest point in more than two years in heavy late selling prompted by the collapse of the Gulf Oil-Cities Service deal and continuing worry about the condition of the economy.

The Dow Jones Industrial Average fell 11.51 to 784.34, its lowest level since it stood at 759.13 on April 21, 1980, closing a week which saw that index of stock activity fall by more than 24 points. Since July 20, the average has plunged more than 49 points. In addition, most other measurements fell this week to new lows for the year, including the Dow Jones Transportation Index, which plunged a total of almost 12 points to 297.06.

The results led analysts to suggest that the market would continue to drop next week. "My feeling is that you're going to continue to have rather violent sessions Monday and Tuesday," said Newton D. Zinder, senior vice president at The E. F. Hutton Group Inc. "The market is quite oversold and the bond market is quite weak, too. There is also no evidence in the economy of an upturn."

Most Wall Street executives continue to be skeptical about the economic upturn, helping to keep the market in sharp decline. "This is a very, very weak economy, with signals almost like a minirecession before a recession," said James Balog, senior executive vice president at Drexel Burnham Lambert Inc. "Interest rates have a long way to go before the stock market comes back. The market is marking time."

But stocks were moving only slightly lower at midday today with the industrial average down 3 1/2 points at mid-afternoon, falling after a slight morning rally. Speculators and arbitrageurs who had bet on completion of the Gulf-Cities Service deal, sold other stocks in heavy trading after midday as word spread that the merger was off.

By the market's close, the losses were broad, although volume dropped to 48.66 million shares from yesterday's 54.7 million. On the New York Stock Exchange, losers outran gainers more than two to one as 970 stocks fell while 448 rose, with seven issues reaching new highs and 116 hitting new lows, and the exchange's composite index dropped 0.75 to 59.69. Cities Service stock dropped by 6 3/4, closing at 37 1/4 and Gulf was up 5/8 at 25 1/2 before trading in both issues was halted at midafternoon pending the news.

Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 56.36 million shares.

Atlantic Richfield was the day's most active issue, off 5/8 at 33 3/4 in trading that included a 1.21 million-share block at 33 3/4.

Standard & Poor's index of 400 industrials fell 1.70 to 115.69, and S&P's 500-stock composite index was down 1.45 at 103.71.

The American Stock Exchange market value index fell 3.13 to 244.99, with volume down to 3.2 million shares. The average Amex share fell 13 cents as 45 stocks reached new lows and only six new highs.