An optically detected magnetic resonance (ODMR) study of the lowest excited state of Pd(2-thpy)(2) ((2-thpy)(-) = 2-thienylpyridinate) in an n-octane Shpol'skii matrix at T = 1.4 K is reported. The results in zero and low magnetic fields allow us to characterize the emissive triplet state in more detail. In this state the spin-orbit contributions to the zero-field splittings of the triplet substates are much more pronounced than for analogous Rh(III) chelate complexes. Microwave recovery experiments display the emission lifetimes of 134 mu s and 1200 mu s of two triplet substates, which are split by 2E = 2886 MHz (0.0962 cm(-1)). The D value characterizing the relative energy of the third sublevel is larger than 6600 MHz (0.22 cm(-1)) and is outside the microwave range of our experimental equipment. However, its decay time can be determined to be 235 mu s. Moreover, phosphorescence microwave double-resonance (PMDR) experiments reveal a spin selectivity in the vibrational satellite lines of the emission spectrum. Such a phenomenon is observed for the first time for transition-metal compounds. The selectivity is a consequence of different mechanisms of radiative vibronic deactivations from the different emissive triplet sublevels.