Nelissen was conscripted in the Medical Corps of the Royal Netherlands Army serving as a Sergeant from September 1956 until October 1957.

Nelissen was elected as a Member of the House of Representatives after the election of 1963, taking office on 5 June 1963 serving as a frontbencher chairing the special parliamentary committee for Right of Inquiries for Companies and spokesperson for Finances, Housing and Spatial Planning, Small business and deputy spokesperson for Economic Affairs.

The Cabinet Biesheuvel I fell just one year later on 19 July 1972 following the withdrawal of the Democratic Socialists '70 (DS'70) because of their dissatisfaction with the proposed budget memorandum to further reduce the deficit and continued to serve in a demissionary capacity until the first cabinet formation of 1972 when it was replaced by the caretaker Cabinet Biesheuvel II with Nelissen continuing as Deputy Prime Minister and Minister of Finance, taking office on 9 August 1972.

After the election of 1972 Nelissen again returned as a Member of the House of Representatives, taking office on 7 December 1972[2] but he was still serving in the cabinet and because of dualism customs in the constitutional convention of Dutch politics he couldn't serve a dual mandate.

In September 1973 he was named as a financial adviser for the AMRO Bank, in September 1979 he was named as chief financial officer (CFO) and vice chairman of the board of directors for the AMRO Bank, in April 1983 he was appointed chief executive officer CEO and chairman of the board of directors for the AMRO Bank.