The stability of an ideally conducting plasma cylinder in a strong, time-dependent magnetic field is studied in the magnetohydrodynamic approximation. When there is no radial movement of particles the configuration is stable (the stability in question is that of a non-rotating plasma column in one longitudinal field, although the current along the cylinder axis and the rotation of the medium are taken into account in some of the sections of this work). The superposition of the time-dependent component of the longitudinal magnetic field may produce the following three types of instability: (1) In a contracting cylinder the long-wave perturbations may become unstable; when this happens the development time is inversely proportional to (|m|−1)½, where m is the perturbation mode. This is an instability of the Rayleigh-Taylor type. The effect is studied by means of a homogeneous plasma column model in which the compression velocity is linearly dependent on the radius and the magnetic pressure distribution is parabolic; (2) In a plasma in which the compression or expansion velocity is of the same order as the thermal speeds, non-radial natural oscillations may build up. In particular, the bands of instability are narrow for cylinder pulsations of small amplitude, while the growth rate is proportional to the amplitude of the pulsations. The most dangerous resonance occurs if the pulsation frequency is close to the sum of the two oscillation freqviencies (or twice the frequency of one oscillation); (3) Instability occurs in an inhomogeneous plasma contained by a strong magnetic field on which a parallel field of small amplitude and high frequency is superposed (it is assumed that the frequency is much greater than the ratio of thermal speeds to plasma column radius). The development time of the perturbations is inversely proportional to the amplitude of the alternating field component and decreases abruptly near frequencies exceeding ion cyclotron frequency. In this region a build-up occurs of highfrequency non-radial natural oscillations that are independent of the co-ordinate along the cylinder. The most stable configuration has a uniform density distribution and a sharp boundary, and the growth rates are proportional to the square root of the ratio of the boundary layer thickness to the cylinder radius. The author suggests that the effect considered in this work is the cause of the high level of diffusion observed at the ion cyclotron resonance.