We prove that a helicodial surface has constant mean curvature if and only if its principal axes make an angle constant with the orbits. Moreover, the arguments used lead to a simple proof of the fact that all helicodial surfaces with constant mean curvature $H$ can be isometrically deformed, trough helicodial surfaces of the same $H$, into surfaces of revolution of the same $H$ (Delaunay surfaces).