In this paper, we address the problem of the strict-sense nonblocking operation of an elastic optical switch. Elastic optical switches are used as nodes in elastic optical networks (EONs), where fine granular frequency slots or flexible grids are used in opposite to the traditional optical networks, where fixed grids are used. The switch architecture considered in this paper consists of waveband converting switches in input and output stages, while in the center stage there is only one wavelength selective space switch without wavelength conversion capabilities. We derive the number of frequency channels k needed in interstage links to ensure the nonblocking operation of the switch when input and output links have n frequency channels and a frequency slot of one connection is not greater than m frequency channels. Both, necessity and sufficient conditions are proved.