  We investigate how the 331 models face new data on B_{s,d}->mu^+mu^- and
B_d->K^*mu^+mu^- taking into account present constraints from Delta F=2
observables, low energy precision measurements, LEP-II and the LHC data. In
these models new flavour violating interactions of ordinary quarks and leptons
are dominated by a new heavy Z^prime gauge boson with the strength of the
relevant couplings governed by four new parameters in the quark sector and the
parameter beta. We study the implications of these models for beta=+-n/sqrt{3}
with n=1,2,3. The case beta=-sqrt{3} leading to Landau singularities for
M_{Z'}approx 4Tev can be ruled out when the present constraints on Z^prime
couplings, in particular from LEP-II, are taken into account. For n=1,2
interesting results are found for M_{Z^prime}< 4Tev with largest NP effects for
beta<0 in B_d->K^*mu^+mu^- and the ones in B_{s,d}->mu^+mu^- for beta>0. As
Re(C_9^NP) can reach the values -0.8 and -0.4 for n=2 and n=1, respectively the
B_d-> K^*mu^+mu^- anomalies can be softened with the size depending on Delta
M_s/(Delta M_s)_SM and the CP-asymmetry S_{psiphi}. A correlation between
Re(C_9^NP) and BR(B_s->mu^+mu^-), identified for beta<0, implies for negative
Re(C_9^NP) uniquely suppression of BR(B_s->mu^+mu^-) relative to its SM value
which is favoured by the data. In turn also S_{psiphi}< S_{psiphi}^SM is
favoured having dominantly opposite sign to S_{psiphi}^SM. We find that the
absence of B_d-> K^*mu^+mu^- anomalies in the future data and confirmation of
the suppression of BR(B_s->mu^+mu^-) relative to its SM value would favour
beta=1/sqrt{3} and M_{Z'}approx 3Tev. Assuming lepton universality, we find an
upper bound |C_9^NP|<1.1(1.4) from LEP-II data for all Z' models with only
left-handed flavour violating couplings to quarks when NP contributions to
Delta M_s at the level of 10%(15%) are allowed.
