Methods of passing through resonance zones in mechanical systems are discussed and a new method based on the speed-gradient energy control of two subsystems (rotor and support) is presented. Two typical problems of passing through resonance for one- and two-dimensional motion of the support are posed and analyzed by computer simulation. The control algorithms based on the speed-gradient method and averaging allow one to significantly reduce the required level of the controlling torque. The proposed algorithms have a small number of design parameters. Compared with the known algorithms the proposed ones are more simple for design and exhibit stronger robustness properties. (C) 2010 Elsevier Ltd. All rights reserved.