  It is shown that the tunneling effect in quantum cosmology is possible not
only at the very beginning or the very end of the 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,
{\it 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 kind of tunneling is given
explicitly. It is inversely related to the amount of nonrelativistic matter
(dust), and grows from a certain fixed value to unity if the negative
cosmological constant approaches zero.
