The magnetic behavior of a series of compounds with general formula RE(hfaC)3NITEt (RE = Tb, Er, Ho; hfac = hexafluoracetylacetonate; NITEt = 2-ethyl-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-l-oxyl 3-oxide) are reported. The presence of lanthanide ions with anisotropic ground states deeply influences the magnetic behavior of these low-dimensional systems. In particular magnetic phase transitions to ordered states are observed. The nature of these transitions is analyzed and the unusually high critical temperatures are related to the anisotropy of the rare earth metal ions. The coupling mechanisms are reconsidered in comparison with those discussed for similar systems where diamagnetic or isotropic metal ions are present.