The present study investigates the spin-orbit coupling (SOC) effects in the radiative processes from the electronically excited states of bis-[2-(2-thienyl)-pyridine] platinum (Pt(thpy)(2)) and palladium (Pd( thpy) 2). The transition probabilities among the low-lying spin-mixed states in these complexes are estimated using the discrete variable representation (DVR) method based on the assumption that the system obeys Fermi's golden rule. It is revealed that the low-lying excited singlets and triplets are strongly mixed with each other by SOC in Pt(thpy) 2 and, as a result, a fast nonradiative transition occurs to the low-lying excited spin-mixed states. This is followed by the radiative transition from these low-lying spin-mixed states to the lowest spin-mixed state (the ground state); that is to say, a phosphorescence should be observed from these low-lying excited spin-mixed states in Pt(thpy)(2). On the contrary, weak SOCs are obtained in Pd(thpy)(2) and no phosphorescence at room temperature is expected to be observed in Pd(thpy)(2). These results are in good agreement with the experimental reports.