Quantum tunneling effect in oscillating Friedmann cosmology

It is shown that the tunneling effect in quantum cosmology is possible not only at the very beginning or the very end of evolution, but also at the moment of maximum expansion of the Universe. A positive curvature expanding Friedmann universe changes its state of evolution spontaneously and completely, without any changes in the matter content, avoiding recollapse, and falling into oscillations between the nonzero values of the scale factor. On the other hand, an oscillating nonsingular universe can tunnel spontaneously to a recollapsing regime. The probability of such kinds of tunneling is given explicitly. It is inversely related to the amount of relativistic matter (dust), and grows from a certain fixed value to unity if the negative cosmological constant approaches zero.