We investigate the influence of the magnetic field on the formation an
d evolution of dense cores in molecular clouds. The model originally p
roposed by Myers & Goodman (1988) is modified in order to take into ac
count the effect of a non-negligible external pressure. We define two
parameters beta and p, which allow to specify the physical quantities
of the system (molecular cloud plus core) with reference to the proces
s of ambipolar diffusion, and the quantities involved in the collapse.
The analysis of three samples with different physical characteristics
suggests a possible interpretation of an evolutionary sequence for th
e condensation originated within a magnetized molecular cloud, towards
the stage of protostar.