We consider the self-calibration problem for a moving camera whose intrinsic parameters are known, except the focal length, which may vary freely across different views. The conditions under which the determination of the focal length's values for an image sequence is not possible, are derived. These depend only on the camera's motions. We give a complete catalogue of the so-called critical motion sequences. This is then used to derive the critical motion sequences for stereo systems with variable focal lengths.