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The party has won 249 of the 489 seats contested in the Lower House, and even with 133 results yet to be declared it is clear that the Congress Party will control the next Parliament.
The victory has earned Pandit Nehru a further five-year term in office. He has led the interim government since 1947, when power passed from British to Indian hands, but this makes him India's first prime minister to be elected by universal suffrage.
The elections are widely seen as a test for India's ability to succeed as a democracy following independence from Britain two years ago.
They are the first to be held under the new constitution, drawn up with the British parliamentary system as a model.
There were fears that extremist groups would use the opportunity to whip up inter-ethnic tensions, but to everyone's relief voting has so far gone peacefully.
The polling operation is on a massive scale.
There are 176 million people eligible to vote, although only 15% can read or write.
Symbols are being used on ballot papers for each of the parties and independent candidates, so that those who cannot read know where to cast their vote.
Voters are not even required to mark their ballot papers - they simply have to put them into a box marked with the symbol of their favoured candidate.
About 18,000 candidates are running for 4,412 seats: 497 in the Lok Sabha, or lower house of parliament, and the rest in state government.
Although the Congress Party, which has been inextricably linked with the drive for independence, has secured an absolute majority in the parliamentary elections, it suffered some unexpected setbacks in state elections.
In three southern states in particular - Madras, Hyderabad and Travancore-Cochin - the party failed to win an outright majority in the face of strong support for the Communist Party.
The result has caused some concern in the Congress Party. The states do not have to follow central government policies, so the Communist Party's strength there could potentially cause the government serious difficulties.
However, two of the most feared militant parties - the Hindu Mahasabha, and the separatist Sikh Akali Party - did so badly that both parties are expected to collapse following the elections.
The Communist Party of India (CPI) continued to be a thorn in the government's side for some years, particularly in the southern states.
In 1957 it was elected to rule the state government of Kerala (formerly Travancore-Cochin and neighbouring Malabar), only to have the government dismissed and President's Rule declared in 1959.
The CPI is now split into several splinter groups.
Although it still has support in Kerala and in some other states, its share of the parliamentary vote has more than halved.
Prime Minister Jawaharlal Nehru governed the country until his death in 1964, and remains a towering figure in independent India's early political history.
The Congress Party, largely led by Nehru family members, continued in an almost unbroken run of power until 1989.
Following a decisive victory in the 1996 elections, the Hindu nationalist Bharatiya Janata Party (BJP) emerged as the strongest party and formed a government under its moderate leader, Atal Behari Vajpayee.]
But in 2004, the Congress Party once again returned to power under former Finance Minister, Manmohan Singh.
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