Theoretical predictions are given for the branching ratios and the CP violating time-integrated asymmetries for the decays into two pseudoscalar mesons of the pseudoscalar neutral particles with definite beauty at t = 0 and strangeness S = 0, +/- 1. For some of the considered decays these asymmetries depend only, or mainly, on the values of the elements of the Kobayashi-Maskawa matrix; the present knowledge about them, in particular the uncertainty on the value of the CP-violating phase-delta, affects the precision of the predictions. As long as the decays of B(d)0 and B(d)0BAR into final states with predicted branching ratios larger than 10(-4) are concerned, positive asymmetries are expected for eta-C K1(0) (in the range from 10% to 37%) and D+ D- (12% to 39%) and a small negative asymmetry for D- pi+ (-0.3% to -2%). The asymmetry for pi+ pi- (from -32% to 47%) shows a strong dependence on the explicit evaluation of the weak amplitude and on the sign of cos-delta. Smaller asymmetries are predicted for the decays of B(s)0 and B(s)0BAR as a consequence of the large value expected for the mixing parameter Z(s) = DELTA-M(s)/GAMMA-s. A negligible effect is found for F+ F- (from - 0.1% to - 0.5%), whereas a larger one occurs for F+/- K+/- (from 1% to 8%) and eta' K1(0) (from - 3% to - 6%).
