  A detailed analysis of the effects of supersymmetric models without R-parity
on various CP asymmetries in neutral $B$ decays is given. We concentrate on
models with Abelian horizontal symmetries that allow us to estimate the order
of magnitude of the new effects. We focus on channels where the Standard Model
gives clean predictions: $ B_{d}\to\psi K_{S} $ and $B_{d}\to\phi K_{S}$. The
two asymmetries can have a value different from $\sin2\beta.$ Moreover, they
can be different from each other.
