The long, dark shadows cast upon Los Angeles' bid to be the host city for the 1984 Summer Olympics come not from Proposition 13, but from the experiences of a foreign city thousands of miles away - Montreal.

As the host city for the 1976 Olympics, Montreal ran afoul of its promises to produce the "cheapest" Games in modern history. Instead, it ran up a deficit of almost $1 billion in construction costs and put on the most expensive Games in modern history.

Montreal's defenders say that if capital improvements are set aside, the city actually made a profit of $118 million. But the exorbitant deficit has had a psycological impact on other cities with lesser financial resources that would like the prestige of having the Games, but not the price tag.

As a result of the financial embarrassment surrounding the Montreal Games, the International Olympic Committee, which awards the Games to cities, wrote a new clause in one of its rules.

The clause says that the selected city and the national Olympic committee for the country - in this case, the U.S. Olympic Committee - must have complete financial responsibility for the operation of the Games.

The rule has been the source of constant, prolonged disputes between the IOC and the City of Los Angeles, which hosted the 1932 Olympics and has an abundance of facilities left from those Games as well as newer ones that are the product of the California recreational boom.

Los Angeles and New York were the only cities in the world to bid for the 1984 Games and Los Angeles,with the USOC's blessing, won conditional approval from the IOC. The condition was that Los Angeles sign the standard IOC contract. That is when the city balked. The standard contract had that new clause the city does not like.

Los Angeles Mayor Tom Bradley, backed by many other city officials, wanted the IOC to waive that new rule to permit a group of private businessmen headed by John C. Argue to assume financial responsibility for the Games along with USOC.

The IOC has so far refused, saying it would set precedent. The IOC's intransigence is generally regarded as little more than face-saving.

Olympic politics aside, Bradley and the private Olympic organizing committee are beset by city and state politics.

On one hand, fans of the Los Angeles Rams are afraid the team would move to Anaheim Stadium permanentl if forced to move out of the L.A. Coliseum while it undergoes some renovations for the Games.

On the other hand, and far more important, is the current taxpayers' revolt in the state that culminated in the passage of Porposition 13, slashing and limiting property taxes.

The passage has no direct effect on the L.A. Olympics since property taxes were not going to be used to finance the Games. But, Proposition 13 has stirred a revolt against government spending and, in some quarters, this has been translated into an anti-Olympics faction.

Last Tuesday, after the IOC again rejected the concept of the private committee, Bradley recommended that the city council withdraw the city's bid. The council has postponed action on his request.

Almost immediately, Lord Michael Killanin, IOc president, suggested that Bradley was being too hasty and offered to extend the contract deadline from July 31 to August 21. Killanin's cable, however, pointedly went to Bradley and not Argue, the head of the private committee.

Bradley, in an interview in Washington late last week, said he thought the IOC was "keeping the door open and that is a sign of hope." He said he would check with the Argue committee before contacting Killanin. From others in L.A. the message was, "No Argue, no Olympics."

Bradley has support in his contention the private committee, together with the USOC, could finance the Games and even turn a profit F. Don Miller and Bob Kane, executive director and president of the USOC, respectively, are confident of a successful Olympics.

To understand their optimism, it must be reemphasized that Los Angeles, unlike Montreal, has a wealth of existing facilities. Capital improvements are estimated at a mere $333 million.

Initial cost estimates for the Games is $183 million and Los Angeles could profit by as much as $100 million to $250 million from television income, ticket sales, corporate agreements and so forth, Miller said.

Bradley said a special hotel-motel tax, estimated to raise almost $5 million, would be used for services, such as security, over and above normal operating costs. Members of the California congressional delegation have indicated they will seek federal funds for the Games. This has been a common procedure in past Olympics.

A meeting with the IOC is the next step and one which is being watched by other cities - including the practically debt-ridden New York - in if the L.A. bid falls through.