The energy gap law established for aromatic hydrocarbons and rare earth ions relates the nonradiative decay rate to the energy gap of a transition through a multiphonon emission process. We show that this energy gap law can be applied to the phosphoresce of a series of conjugated polymers and monomers for which the radiative decay rate has been enhanced through incorporation of a heavy metal. We find that the nonradiative decay rate from the triplet state T-1 increases exponentially with decreasing T-1-S-0 gap for the polymers and monomers at 300 and 20 K. Comparison of the nonradiative decay of polymers with that of their corresponding monomers highlights the role of electron-lattice coupling.