HOUSTON, JULY 11 -- Even as the leaders of the Western democracies celebrated the end of the Cold War today and offered encouragement to Soviet President Mikhail Gorbachev, they displayed sharply differing assessments of Gorbachev's prospects -- and how the West should respond to his appeal for help.

They agreed on what one U.S. official called "the lowest common denominator," ordering a six-month evaluation of the Soviet economy, coupled with expressions of support for the Soviet reform effort and demands that it go much further.

But in their explanations of what they had done here, the leaders reflected the varying agendas and outlooks about Gorbachev that they brought with them to Houston. They each had differing interpretations of what would follow the study at the end of this year, and they decided to let each nation go its own way for now. "Some countries are already in a position to extend large-scale financial credits," the leaders noted in their final declaration.

Often united in the past by the threat of Soviet aggression, the leaders of the United States, Britain, France, West Germany, Italy, Canada and Japan spent much of the three-day summit in a philosophical debate about what the future holds for Gorbachev. It sounded like a family argument around the kitchen table about whether the repentant neighborhood bully should get a helping hand or still be viewed with extreme caution.

President Francois Mitterrand of France took the lead in trying to convince the others that Gorbachev deserves an urgent response from the West. "It does not make much sense if aid materializes when political reforms have failed and we have waited too long," he told reporters. Mitterrand expressed impatience with the demands of the United States, Japan, Britain and Canada that a host of political issues be settled as a condition for direct financial aid, such as termination of Moscow's support for Cuba, or return of the disputed Northern Territories to Japan.

"Taking all that together," he said of the demands of his summit partners, "this doesn't mean as much urgency as I would have hoped."

Mitterrand said Gorbachev is a better investment than what could follow if reform fails. "There are more safeguards than the unknown," he said when asked about the risks of putting too much stock in Gorbachev. "This kind of problem will have to be dealt with whoever is the leader. We think it is important to help a man . . . who has made so many changes. We'll continue to reckon with Russia because Russia will continue to exist."

West German Chancellor Helmut Kohl, who has proposed a $15 billion joint Western aid package and will visit Moscow next week, put the most optimistic face on the possible outcome of the six-month study. "My prognosis is that the necessary steps are being initiated in the Soviet Union," Kohl said. "If this continues, by the end of the year, we should be able to achieve a joint Western economic assistance program."

Kohl expressed some sympathy with the complaint from other leaders that aid to Moscow might not be popular at home. "I'm not Father Christmas who can just give away taxpayers' money. We have obligations to account for," said Kohl, whose government has already guaranteed a $3 billion line of credit to Moscow.

Gorbachev wrote to President Bush recently asking for large-scale, long-term credits from the West, and Kohl said the six-month study should not embarrass Moscow. "We're not talking about humiliating them. That would be foolish."

While Bush continued to promise technical aid to Moscow, such as experts in transportation, capital markets, legal systems and distribution of goods, the president stood his ground against direct aid. Asked if Gorbachev can expect U.S. participation in a financial effort in six months, Bush responded, "Not particularly. Not necessarily." He said U.S. aid to Moscow is "not in the cards" at this time.

British Prime Minister Margaret Thatcher also expressed doubt whether the study would automatically lead to Western assistance for Moscow. "You are really putting the cart before the horse if you ask me what we expect to come out of it and what would be the result after we had it," she said.

Bush, joined by Japanese Prime Minister Toshiki Kaifu, Canadian Prime Minister Brian Mulroney and Thatcher, repeatedly insisted on conditions to a Western aid effort. They pushed for language in the final declaration linking Western aid to further efforts by Moscow to "shift resources substantially away from the military sector and to cut support to nations supporting regional conflict."

Mulroney said, "I don't think it's offensive to say to somebody who appears to be pretty broke" that it's "not such a smart idea" to ask for money "and then fork it over to the Cubans."

In a news conference today, Bush seemed to expand these demands, linking economic aid to progress in arms control. "I'm not particularly enthusiastic about the intercontinental ballistic missiles aimed at U.S. cities," he said. "A good way to start in doing something about that is to have a successful conclusion" to the negotiations on a new strategic arms treaty.

While Mitterrand and Kohl argued the urgency of Gorbachev's cause, Bush appeared more sanguine, noting the Soviet president's "landslide" victory in the party congress. "He's in the political arena and he did pretty darn well," Bush said.