In the first of the two programmes, the Justice Secretary Michael Gove will answer questions on the case to leave the EU to a Question Time audience in Nottingham. This programme will broadcast on Wednesday 15 June.
Four days later, on Sunday 19 June, the Prime Minister David Cameron will take questions on the arguments to retain EU membership. This programme is live from Milton Keynes.
Question Time will be moderated by David Dimbleby, and both programmes will be screened in the early evening to reach as wide an audience as possible.