The world's two largest democracies are natural companions, no matter who their other friends may be. So it is welcome that the United States and India are warming chilly relations with a meeting between President Reagan and Prime Minister Gandhi this week - even though the US doesn't like India's ties with Moscow, and India doesn't like Washington's rearming of Pakistan.
There have been many ups and downs since Mrs. Gandhi's last visit a decade ago. But she and Mr. Reagan are said to have gotten along well at the Cancun summit on third-world development last fall. The immediate fruit of their visit now could be a setting of the seal on mutual good will. To establish such a tone could ease remaining points of friction as well as foster future cooperation.
Washington has been taking note of India's efforts to prepare the way. For example, India has muted its criticism of the US arms for its adversary Pakistan voted by Congress last year. It has tried to show that its friendship treaty with the Soviet Union - and failure to condemn the Soviet invasion of Afghanistan - does not mean that India has abandoned nonalignment to join the Soviet camp. It has reacted with deliberate restraint to the US cutoff of nuclear fuel; that is, instead of scuttling long-standing nuclear agreements, India has continued to abide by them pending renegotiation.
In any case, good relations with India recommend themselves to Washington since India is a big country in a strategic part of the world.
It is really not enough for Mrs. Gandhi to excuse India's position on Afghanistan by saying that it did not want to condemn the Soviets on this issue because ''similar actions by other countries in other parts of the world have not been condemned.'' But her reluctance to alienate the nearby superpower can be understood. Moscow not only provided India with much industrial equipment in years when Washington declined to do so; it also helped India build up its military defenses with highly favorable coproduction deals that have permitted India to develop its own technology.
But Mrs. Gandhi and her country know, even though they don't trumpet it, that the United States deserves credit for helping Indians help themselves in another way. US aid bolstered the ''green revolution'' that speeded India toward increased food production. Perhaps self-sufficiency cannot be claimed - unless calorie counts are placed low and interruptions for bad harvests are discounted. But there is enough to prevent famine in India's enormous population.
While the problems of high population abound, there are also remarkable signs of economic growth, especially in the middle class and private sector. Observers speak of both economic and cultural excitement contrasting with the public laments about political corruption and decline of moral values that were issues in the recent presidential campaign. Some see these as perennial topics in India - a little like ''things aren't what they used to be'' in the US - without any extraordinary excesses at the moment. However, Mrs. Gandhi did take some measures for preventive detention and curbing labor strikes that roused apprehensive memories of the repression that led to her ousting from power during the 1970s.
Certainly Americans will want to be assured that the prime minister's government is practicing the democracy it proclaims. They will want to be sure her nonalignment is not just skin deep. But there is no reason that they and their leaders should not be open to her new friendly overtures - or should not listen sympathetically to the pleas she is expected to bring for a renewal of US aid to the developing world in the spirit with which America helped her country and so many others in the past.