Spin-lattice relaxation times T1 of photoexcited triplets (3)C70 in glassy decalin were obtained from electron spin echo inversion recovery dependences. In the range 30-100 K, the temperature dependence of T1 was fitted by the Arrhenius law with an activation energy of 172 cm(-1). This indicates that the dominant relaxation process of (3)C70 is described by an Orbach-Aminov mechanism involving the higher triplet state t2 which lies 172 cm(-1) above the lowest triplet state t1. Chemical modification of C70 fullerene not only decreases the intrinsic triplet lifetime by about ten times but also increases T1 by several orders of magnitude. The reason for this is the presence of a low-lying excited triplet state in (3)C70 and its absence in triplet C70 derivatives. The presence of the higher triplet state in C70 is in good agreement with the previous results from phosphorescence spectroscopy.