This dissertation consists of three parts. In Part I, it is shown that looping trajectories cannot exist in finite amplitude stationary hydromagnetic waves propagating across a magnetic field in a quasi-neutral cold collision-freeplasma. In Part II, time-dependent solutions in seriesexpansion are presented for the magnetic piston problem,which describes waves propagating into a quasi-neutral coldcollision-free plasma, ensuing from magnetic disturbanceson the boundary of the plasma. The expansion is equivalentto Picard's successive approximations. It is then shownthat orbit crossings of plasma particles occur on the boundary for strong disturbances and inside the plasma for weak disturbances. In Part III, the existence of periodic waves propagating at an arbitrary angle to the magnetic field in a plasma is demonstrated by Stokes expansions in amplitude. Then stability analysis is made for such periodic waves with respect to side-band frequency disturbances. It is shown that waves of slow mode are unstable whereas waves of fast mode are stable if the frequency is below the cutoff frequency. The cutoff frequency depends on the propagation angle. For longitudinal propagation the cutoff frequency is equal to one-fourth of the electron's gyrofrequency. For transverse propagation the cutoff frequency is so high that waves of all frequencies are stable.
