  We investigate the formation and evolution of isothermal collapse
nonuniformity for rotating magnetic interstellar clouds. The initial and
boundary conditions correspond to the statement of the problem of homogeneous
cloud contraction from a pressure equilibrium with the external medium. The
initial uniform magnetic field is collinear with the angular velocity. Fast and
slow magnetosonic rarefaction waves are shown to be formed and propagate from
the boundary of the cloud toward its center in the early collapse stages. The
front of the fast rarefaction wave divides the gas mass into two parts. The
density, angular velocity, and magnetic field remain uniform in the inner
region and have nonuniform profiles in the outer region. The rarefaction wave
front surface can take both prolate and oblate shapes along the rotation axis,
depending on the relationship between the initial angular velocity and magnetic
field. We derive a criterion that separates the two regimes of rarefaction wave
dynamics with the dominant role of electromagnetic and centrifugal forces.
Based on analytical estimations and numerical calculations, we discuss possible
scenarios for the evolution of collapse nonuniformity for rotating magnetic
interstellar clouds.
