We study the time dependent CP asymmetries in B-d,s(0), decays in the
left-right model with spontaneous breakdown of CP. Because of the new
contributions to B-0-(B) over bar(0) mixing, the CP asymmetries can be
substantially modified. Moreover, there can be significant new contri
butions to the B-meson decay amplitudes from the magnetic penguins. Mo
st promising for detection of the new physics in the planned B factori
es is that the CP asymmetries in the decays B --> J/psi K-S and B -->
phi K-S which are supposed to be equal in the standard model can diffe
r significantly in this class of models independently of the results i
n the measurements of B --> X-s gamma.