  We develop a formalism wherein the solution of the equations of equilibrium
for a self-gravitating, magnetized interstellar cloud may be accomplished
analytically, under the only hypotheses that (a) the cloud is scale-free, and
(b) is electrically neutral. All variables are represented as series of scalar
and vector spherical harmonics, and the equilibrium equations are reduced to a
set of coupled algebraic equations for the expansion coefficients of the
density and the magnetic vector potential. Previously known axisymmetric
solutions are recovered and new non-axisymmetric solutions are found and
discussed as models for pre-protostellar molecular cloud cores.
