The purpose of this work was to determine the relative efficiencies of new Nd3+-doped laser active/Raman - tungstate, molybdate, and fluoride - materials (SrWO4, PbWO4, BaWO4, SrMoO4, PbMoO4, SrF2, and LaF3) under selective longitudinal optical pumping by the alexandrite (~750nm), or diode (~800nm) laser. Crystals with various length, orientations and active ions concentrations were tested. To optimize the output of the tested lasers a set of input dichroic and output dielectric mirrors with different reflectivities were used. For realized lasers operating at pulsed free-running regime, threshold energy, slope efficiency, emission wavelength, and radiation polarization were determined. For each crystal, fluorescence lifetime and absorption coefficient under given pumping were established. The slope efficiency in case of Nd3+:PbMoO4 laser at wavelength 1054nm was measured to be 54.3% with total efficiency of 46% which is the best result obtained for all new tested crystals. For Nd3+ doped SrWO4, PbWO4, and BaWO4 crystals simultaneous laser and self-Raman emission were demonstrated in Q-switched regime. Thus newly proposed laser Raman crystals demonstrate high efficiency for Nd3+ laser oscillations comparable with well known and widely used Nd:KGW crystal. Further improvement in the quality of tungstate and molybdate type crystals should result in further increase in lasing efficiency at 1.06μm wavelength. Self Raman frequency conversion of Nd3+-laser oscillations in these crystals should result in high efficient pulse shortening, high peak power and new wavelengths in 1.2-1.5μm wavelength region.