In supersymmetric theories, where the Peccei-Quinn mechanism is called for for the solution of the strong CP problem, the requirement that the density of the universe is critical opens the possibility of dark matter made of axinos, the fermionic partners of the axions. In turn this sets severe constraints on photino and sfermion masses and on R -parity violation. The resulting spectral distribution of axinos is non-thermal. For a thermal distribution, the expected range of axino masses might allow an agreement with a cold dark matter model. The distribution we find seems to make it somehow harder to reconcile axinos with such a cosmological picture.