We developed models for unary nucleation of water and carbon dioxide in the Martian atmosphere. Both homogeneous and heterogeneous nucleation on dust particles were studied. Our models are based on classical theory. We compare results of different adsorption approaches. Heterogeneous nucleation on the abundant dust particles seems to be the primary mechanism of both H2O and CO2 cloud formation in the Martian atmosphere. Heterogeneous nucleation is obtained at a saturation ratio of about 1.18 for H2O and 1.32 for CO2. Homogeneous nucleation is not likely to occur since it would require high supersaturations. We use our models to study nucleation as a function of height at different locations on Mars where ice fog or clouds have been observed. H2O ice nucleation results are in good agreement with surface fog observations and previous model studies. CO2 ice nucleation simulations in the polar hood cloud areas suggest that negative temperature perturbations caused by, e.g., adiabatic cooling in orographic waves or in convective plumes are required for the formation of CO2 clouds.