Magnetic linear dichroism (MLD) spectroscopy is a relatively new technique which previously has been almost exclusively applied to atoms. These investigations have revealed that the study of MLD, in conjunction with electronic absorption and magnetic circular dichroism (MCD) spectroscopies, provides significant additional information concerning the electronic structure of atoms. More recent measurements have indicated that MLD is also observable from transition ions in inorganic compounds and metalloproteins. While the theory for atomic MLD has been worked out in considerable detail during the last two decades, an MLD theory of practical utility for the analysis of the spectra derived from the majority of paramagnetic molecules is not available. In the present contribution, the MLD of an electric-dipole-allowed transition between twofold-degenerate molecular spin levels is analyzed, assuming nonsaturating conditions. As for atomic systems, it is found that the MLD of a single molecule is dominated by the term G(0). However, this term vanishes in the powder average evaluated for a randomly oriented ensemble of molecules, leading to a drastic reduction of the MLD differential absorption for systems with spin S=1/2 compared to that observed for systems with higher ground-state spin. It is found that MLD and MCD spectroscopies on solution samples have complementary spin-state specific sensitivities which suggest that the two methods can be used to selectively probe the individual metal sites in multicenter metalloprotein assemblies.