Rayleigh‐Taylor (RT) instability developing in a layer of matter accelerated by magnetic pressure is shown to be suppressed if the accelerated layer scoops unperturbed matter, entraining it into motion. This stabilizing mechanism is effective for multicascade systems like explosive generators of high pulsed magnetic field or multiple (nested) gas‐puff Z‐pinches, where unperturbed elements are successively involved into accelerated motion. Linear stability analysis of one‐dimensional solutions of the piston problem demonstrates that perturbation of the given wavelength &lgr; does not grow appreciably until the thickness of the accelerated layerL(t) exceeds &lgr;. Before that, if acceleration is increased rapidly enough, amplitudes of the long‐wavelength perturbations remain almost constant and an oscillatory eigenmode localized near its front surface. If acceleration is increased not too rapidly, stays constant, or is decreased, then the long‐ wavelength perturbations with&lgr; > 2L(t)are damped. For the case when acceleration of the first shell is reversed in collision, short‐wavelength perturbations are stabilized. The optimal mass ratio is estimated for a double gas‐puff Z‐pinch: The inner shell must be ∼ 3 times heavier than the outer one.