[en] The Einstein-Cartan theory of gravitation allows for avoiding singularities. This idea is supported by giving exact solution of cosmological equations which are extensions of the Friedmannian cosmology. Various singularity-free models of dust and radiative universes are constructed. Two general relations are given which allow for a transition from dust-filled to radiation-filled universes with the same value of the scale factor. These relations are characteristic of the Einstein-Cartan theory, and cannot be brought over into general relativity. It is shown how exact solutions of the Einstein-Cartan theory can be derived from known solutions of general rela tivity. This procedure which may be applied to material spheres, is simple enough to generate a large set of useful solutions. Two examples are given. (author)