General expressions are presented for the important terms in the magnetic circular dichroism (MCD) and magnetic linear dichroism (MLD) spectra of randomly oriented, rigidly fixed linear molecules in the low magnetic field limit. Attention is concentrated specifically on the signs expected for the differential absorbance in MCD and MLD for ΔΩ = 0 or ±1 electronically allowed transitions. It is found that for paramagnetic linear molecules the important MCD C0 terms are negative, absent and positive for ΔΩ = +1, 0 and -1, respectively, while the MLD G0 terms are negative, positive and negative for the same order of ΔΩs. Other magneto-optical terms are considered for diamagnetic linear molecules. Used in combination, MCD and MLD spectra of linear molecules such as transition metal dimers in rare gas matrices can provide for an unambiguous assignment of the electronically allowed transitions.