Theory predicts that a compound whose structure possesses both rod-like and disc-like characteristics should exhibit a biaxial nematic phase. With this in mind we have synthesized and characterized two new series of non-symmetric dimers containing rod-like and disc-like mesogenic units linked by a flexible spacer. The two series differ in that in one the perimeter of the disc-like unit is decorated with alkyl chains, whereas for the other it is not. The liquid crystalline properties of the two series were investigated both as pure systems and in their equimolar binary mixtures with an electron acceptor. The nematic phase formed by the equimolar binary mixtures is monotropic. However, a small entropy change at the nematic-isotropic transition could be determined. The nature and structure of the monotropic nematic phase is discussed.