Microwave and magnetic properties of low-dimensional KEr(MoO4)2, CsEr(MoO4)2, and KTm (MoO4)2, single crystals are investigated in paramagnetic region. Microwave absorption spectra are studied at temperatures 1.7-10K in 18-190GHz frequency range. The strong anisotropy of g-factors of the lowest energy levels of rear-earth ions is detected. When external magnetic field is applied along c-axis peculiarities in absorption spectra has been found in all investigated compounds at temperature 1.8 K. The similar peculiarities was observed in the dependencies of the differential magnetic susceptibility on the external magnetic field. The totality of experimental data analysis shows that observed anomalies are due to a structural phase transition induced by applied magnetic field. Different models of description for the observed phase transitions are discussed. An explanation founded on a competition of elastic energy and magnetic one and also a strong g-factor anisotropy is offered.