An osmotic system, in which the pure solvent is coexisting with a solution, has been treated where phase transitions of the permeable component are allowed to occur. In case, that the osmotic pressure is constant, the equilibrium curve describing the temperature dependence of the concentration of the solution is predicted to have discontinuous slopes at the transition temperatures of the pure solvent. In all cases discussed, an increase of the impermeable solute in the solution has to take place above the boiling point and below the melting point of the pure solvent. At constant composition of the solution a sharp drop of the osmotic pressure to zero values is predicted in the temperature ranges adjacent to the liquid state of the solvent. Model calculations by use of a modified Flory-Huggins equation for the system PEG/water demonstrate this effect. The phenomenon is also of importance for natural osmotic systems if the temperatures of the system are changed to the range where water crystallizes.