After his first two national election victories, Prime Minister Narendra Modi of India easily set his own terms, with his Bharatiya Janata Party winning clear majorities.

The result was different in this vote. It was still a victory, but one that left him dependent on a host of coalition partners — particularly on two other politicians from regional parties who could make or break Mr. Modi’s ability to form a government.

Of the more than a dozen parties that make up the B.J.P.’s coalition, known as the National Democratic Alliance, most won just one or two seats. The partners that Mr. Modi needs the most are avowedly secular and removed from his Hindu-nationalist ideology.

Cameras on Wednesday were following every word, meeting and movement of the leaders of the two parties, N. Chandrababu Naidu of the Telugu Desam Party, and Nitish Kumar of Janata Dal-United, whose combined 28 seats in Parliament the prime minister needs to stay in power and push through his agenda.

Here is what to know about the men who have unexpectedly found themselves as kingmakers, and about the parties they lead.

Their parties don’t share Mr. Modi’s Hindu-first agenda.

Though some of the members of the B.J.P.’s coalition this year share Mr. Modi’s hard-line vision, both the Telugu Desam Party and Janata Dal-United are moderate, secular parties that have a diverse support base.