The effect of using Ba2+ to modify the structure and dielectric and piezoelectric properties of Pb(1-x)Bax(Mg1/3Nb2/3)(m)(Zn1/3Nb2/3)(y)(Ni1/3Nb2/3)(n)TizO3(x=0-0.15) ceramics near the morphotropic phase boundary has been investigated. It is found that increasing the content of Ba2+ leads to a sequence of structural transformations from heterophase state (tetragonal and pseudocubic phases) to a cubic state via an intermediate pseudocubic phase. The evolution of the dielectric and piezoelectric properties (sequences of transformations: normal ferroelectric relaxor ferroelectric paraelectric) is shown. It is stated that ceramics with x=0.025-0.050 possess the optimal combination of functional parameters for use in low-frequency receivers and actuators. They are characterized by high values of small-signal and large-signal piezoelectric coefficients d(33) of 621pC/N and similar to 1500m/V (at E=5kV/cm), respectively, and also by increased values of dielectric permittivity epsilon/epsilon(0) and tunability coefficient (?=[(epsilon/epsilon(0)(E=0)-epsilon/epsilon(0)(E0))/epsilon/epsilon(0)(E=0)]100%), equal to similar to 7000 and similar to 80%, respectively (at E=20kV/cm). It is shown that for the creation of high-power piezoelectric transducers it is necessary to use ceramics with x=0.125, which differs with high values of the mechanical quality factor Q(m) and epsilon/epsilon(0) (1406 and 10890, respectively).