He had two sons, Larry and John and two daughters, Linda and Jane.

During his term as Mayor, he would welcome Queen Elizabeth and her husband the Duke of Edinburgh to the city in 1957, a visit which included a ceremony to commence construction of the Queensway superhighway project.

In 1958, Nelms saw the opening of a new city hall facility on Green Island.

He was also chair of the Ottawa Transportation Commission under whose watch electric streetcar transit service was replaced with buses.

Nelms died in Ottawa at Grace Hospital aged 94.