  We consider a nonsingular deflationary cosmological model with decaying
vacuum energy density in universes of arbitrary spatial curvature. Irrespective
of the value of $k$, the models are characterized by an arbitrary time scale
$H_I^{-1}$ which determines the initial temperature of the universe and the
largest value of the vacuum energy density, the slow decay of which generates
all the presently observed matter-energy of the universe. If $H_I^{-1}$ is of
the order of the Planck time, the models begin with the Planck temperature and
the present day value of the cosmological constant satisfies
$\Lambda_I/\Lambda_0 \simeq 10^{118}$ as theoretically suggested. It is also
shown that all models allow a density parameter $\Omega_0 <2/3$ and that the
age of the universe is large enough to agree with observations even with the
high value of $H_0$ suggested by recent measurements.
