A theory for quantum-mechanical calculations of cross sections for atom-molecule and molecular collisions in a magnetic field is presented. The formalism is based on the representation of the wave function as an expansion in a fully uncoupled space-fixed basis. The systems considered include S-1-atom-(2)Sigma-molecule, S-1-atom-(3)Sigma-molecule, (2)Sigma-molecule-(2)Sigma-molecule, and (3)Sigma-molecule-(3)Sigma-molecule. The theory is used to elucidate the mechanisms for collisionally induced spin depolarization. (C) 2004 American Institute of Physics.