We derive a Pauli-Schrödinger type equation from the classical Liouville equation, for a neutral particle with arbitrary spin and magnetic dipole. Our derivation does not apply to a general classical phase-space distribution. Nevertheless, in certain particular cases we show that there is a correspondence between the classical equations and the Pauli-Schrödinger equation. Consequently, the results of the Stern-Gerlach, and also the Rabi type molecular beam experiments, can be interpreted classically, that is, in such a way that the particles have well-defined and continuous trajectory, and also continuous orientation of the spin vector. Theoretical and experimental implications of this conclusion are briefly commented.