The heterogeneous phase transition of four organic vapors and water vapor on a cold substrate was studied by either slowly cooling a substrate or by accumulating vapor under reduced-pressure conditions. At low vapor pressures a solid condensate formed directly on the substrate. At higher vapor pressures, liquid condensate usually appeared first, followed either by 1) subsequent formation of solid crystals independently from the liquid phase (subsequent solidification) or 2) rapid freezing of the liquid condensate (subsequent freezing). Subsequent freezing occurred in a wider temperature range than did the subsequent solidification. A new phase transition model is proposed, based on the equilibrium phase diagram and the measured relationship between critical vapor pressure and temperature for solid condensate formation. The proposed model explains the experimental results quite well. Liquid condensate always forms at critical supersaturation ratios close to unity. The critical vapor pressure and temperature at the boundary separating the formation of the solid condensate from formation of the liquid condensate, as determined by the proposed model, agrees well with the experimentally determined values.