We address the question of universes inside a Λ black hole which is described by a spherically symmetric globally regular solution to the Einstein equations with a variable cosmological term Λμv, asymptotically Λgμv as r → 0 with Λ of the scale of symmetry restoration. Global structure of spacetime contains an infinite sequence of black and white holes, vacuum regular cores and asymptotically flat universes. Regular core of a Λ white hole models the initial stages of the Universe evolution. In this model it starts from a nonsingular nonsimultaneous big bang, which is followed by a Kasner-type anisotropic expansion. Creation of a mass occurs mostly at the anisotropic stage of quick decay of the initial vacuum energy. We estimate also the probability of quantum birth of baby universes inside a Λ black hole due to quantum instability of the de Sitter vacuum. © 2001 Elsevier Science B.V.