Let C be a class of modules and L = lim C the class of all direct limits of modules from C. The class L is well understood when C consists of finitely presented modules: L then enjoys various closure properties. We study the closure properties of L in the general case when C is arbitrary class of modules. Then we concentrate on two important particular cases, when C = add M and C = Add M, for an arbitrary module M. In the first case, we prove that L is the class of all tensor products of L with flat modules over the endomorphism ring of M. In the second case, we show that L is the class of all contratensor products of M, over the endomorphism ring of M endowed with the finite topology, with contramodules that can be obtained as direct limits of projective contramodules. For modules M from various classes of modules (e.g., for pure projective modules), we prove that lim add M = lim Add M, but the general case remains open.