Crystallization of heterospin bischelate NiL2, where L is deprotonated nitroxide 4-(3',3',3'-trifluoromethyl-2'-oxopropylidene)-2,2,5,5-tetramethyl-3-imidazoline-1-oxyl, with alcohols allows a logical assembly of layered [NiL2(CH3OH)(2) (1) and NiL2(C2H5OH)(2) (2)] or frame compounds [NiL2(HO(CH2)(4)OH) (3) and NiL2(HO(CH2)(5)OH) (4)]. The structures of complexes 1, 2, and 4 have been determined. Crystal data : 1, monoclinic, space group P2(1)/c, a = 8.929(2) Angstrom, b = 15.773(3), c = 11.518(2), beta = 118.84(1)degrees, Z = 2; 2, monoclinic, space group P2(1)/c, a = 9.923(5) Angstrom, b = 15.992(5) Angstrom, c = 11.486(2) Angstrom, beta = 120.63(3)degrees, Z = 2; 4, monoclinic, space group C2/c, a = 21.028(4) Angstrom, b = 10.943(2), c = 14.405(3), beta = 110.61(3)degrees, Z = 4. The structure of 3 is very close to the structure of 4 and has been reported earlier. Robust H-bonding between the OH groups of the coordinated alcohols and the >N-O-. groups of the neighboring fragments NiL2 leads to the formation of polymeric layers in the solid. At the same time, hydrogen bonds form effective channels for magnetic interactions >N-O-. ... H-O-R-Ni2+-O-R-H ... O-.-N<. The magnetic phase transition to the weak ferromagnetic state below 7 K is inherent in 1-4. For 2 and 4, this transition is induced by the external magnetic field that correlates with the elongation of Ni-O-R and O-R ... O-.- distances in the exchange channels >N-O-. ... H-O-R-Ni2+-O-R-H ... O-.-N< in solids 2 and 4 compared to 1 and 3. It has been found that magnetic ordering occurs only within the polymeric layers formed due to multiple hydrogen bonds. Investigation of the anisotropy of magnetic susceptibility performed on large single crystals of 1-4 revealed an essentially different ordering of the magnetic moments of magnetic sublattices in 1, 2 and in 3, 4.