The entropy of mixing is calculated for two nonideal two-dimensional mixtures. System I consists of two different monomers with nearest-neighbor interactions between different monomers, and system II of monomers and tetramers without interactions. The entropies of mixing are evaluated exactly for strips of various heights. An extrapolation technique is introduced to obtain approximate results for infinite systems. In both cases the entropy of mixing is decreased compared to the ideal solution. For system I it remains symmetric with respect to the concentration $c=0.5$ and shows a characteristic dip for sufficiently large interactions. The decrease in system II is asymmetric. It is much larger for high tetramer concentrations than for high monomer concentrations.