The dissertation is dedicated to electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) study of structural phase transitions, structural phases and dynamic effects in hybrid metal-formate frameworks. The continuous-wave EPR experiments allowed to characterize the order of the structural phase transitions and motion of the molecular cations in the disordered phases of [(CH3)2NH2][Zn(HCOO)3], [CH3NH2NH2][Zn(HCOO)3] and [NH3(CH2)4NH3][Zn(HCOO)3]2 hybrid frameworks. EPR measurements with an external electric field revealed non-ferroelectric nature of the dimethylammonium zinc-formate, while [NH4][Zn(HCOO)3] framework proved to be ferroelectric. The pulsed EPR spectroscopy allowed to probe the motion of the methyl groups in the ordered phases as well as the lattice dynamics in the vicinity of the structural phase transitions in zinc-formate frameworks. The pulsed ENDOR experiments verified the proton positions in the structural models of these compounds