New Delhi — Three years into a five-year term, India's Indira Gandhi has begun to ride a political roller-coaster. After two stunning defeats last month for the prime minister's party in southern state elections, Mrs. Gandhi claimed a victory Sunday in New Delhi municipal elections. Next Monday, her future prospects are again put to an election test in the beleaguered northeastern state of Assam.
At the same time, she succeeded last week in having her son, Rajiv, placed in a leading post of the ruling Congress (I) Party (the ''I'' stands for Indira).
''Indian politics are now more volatile, less predictable than they've been in the past,'' one foreign official said. ''Mrs. Gandhi has a long way to go before the next parliamentary elections (which must be held not later than January 1985). In the past, there have been a lot of surprises in this country. . . .''
In eight state contests since 1981, Congress has been unable to win a majority. For Mrs. Gandhi, who has made each contest a referendum on her own charisma and her prestige, the state losses registered as a personal defeat.
An indefatigable campaigner, Mrs. Gandhi goes to Assam this week to campaign for an election that few people seem to want. It is being boycotted by all parties, except the Marxists and Congress (I), and has required heavily-armed police to maintain order during the campaign.
Assamese students, who have kept the state in the grip of violence for three years, are agitating against the presence - and voting privileges - of nearly four million illegal aliens from Bangladesh. The government puts the number of illegal immigrants at about 600,000.
Despite bloodshed over the election, Mrs. Gandhi will not call it off. To do so, in the view of those closest to her, would be yet another political setback. The election was called since the Indian government can not legally extend its present one-year direct rule beyond March without Parliament's permission.
Sunday's win in New Delhi for the Congress (I) party in New Delhi is far less significant than it is symbolic. The results should not be interpreted, according to diplomats here, as a progenitor of Mrs. Gandhi's support in the north. For New Delhi, as most capital cities, is not a bell-weather for the nation at large.
It has India's third highest rate of literacy - 61 per cent. In particular, the caste factor, so important elsewhere in northern India, is much less significant here. And New Delhi is also home to a large number of minorities - untouchables, Muslims and Sikhs - which have traditionally given their support to Congress (I).
The New Delhi return have nonetheless been a morale booster for the flagging fortunes of Congress (I). They could also give Mrs. Gandhi a freer hand in dealing with factionalism at the state level and with corruption in the ruling party.