Born to a Jewish family in Amsterdam, Max was a jazz harmonica player who had played with Django Reinhardt in Paris in the 1930s.

When the German Army invaded France in May 1940, Max escaped to England and served, throughout the war, in the Princess Irene Brigade of the Dutch Army in Britain. He was injured during the Normany landings and later discovered parents and sister had been sent to Nazi death camps. They were never heard from again.

After the War, Geldray settled in England and obtained British citizenship. Like The Ray Ellington Quartet, he performed in nearly every Goon Show episode. He occasionally had a few speaking lines in some shows and was often reffered to as "Conks" due to the size of his nose.

After The Goon Show, he emigrated to California and became active in the Christian Science Movement. He was married twice and had one son (Philip) and two stepdaughters (Judy and Holly) with his second wife, Susan.