Transient triplet EPR spectra of two types of spirans, spiro[9,10-dihydro-9-oxoanthracene-10,2’-benz[f]indan] and spiro[9,10-dihydro-9-oxoanthracene-10,2’-3H-phenalene],were measured in a glassy matrix at 77 K. Spin polarization conservation during the intramolecular triplet-triplet energy-transfer process was observed. The results clearly indicate that spin orientation is conserved in the molecular frame in the presence of an external magnetic field and that the high-field approximation cannot explain the spin polarization pattern observed in the X-band EPR spectra. The results contribute to the understanding of the relaxation processes of the excited states.