The development of optimal control strategies for cyclorotor wave energy converters (WECs) is at an early stage. In this paper, we present new methods and solutions for optimal pitch and/or rotational velocity control strategies for different configurations of cyclorotor-based WECs, in both monochromatic and panchromatic waves. The cyclorotor is modelled with the use of an approximate two-dimensional mathematical model, where hydrofoils are approximated as point source vortices in potential waves. The goal of the developed control strategy is to determine the optimal velocity profile, and/or pitch angle variations, for maximum energy conversion, in terms of generated mechanical shaft power. The solutions, obtained with the use of spectral methods, show a clear benefit in using a variable velocity for cyclorotors with either one or two hydrofoils, in monochromatic waves, with a typical increase in energy capture of 30-40%, while the optimal pitching did not significantly increase the value of the absorbed wave energy. We also present control results for panchromatic waves, assuming all the properties of incoming wave packages, within a 10 s time interval, are known. The obtained solutions have shown significant benefit in joint optimal pitch and velocity control, especially in the case of panchromatic waves. It has been also shown that successful implementation of cyclorotor control strategies requires optimal configuration of the static characteristics of the cyclorotor. In conclusion, we discuss the optimal control benefits and highlight problems which must be solved for further successful development of these control strategies.