Phosphorescence and delayed fluorescence of polyfluorene polymer films doped with cyclooctatetraene (COT) and anthracene are studied by means of time-resolved photoluminescence (PL) measurements. The occurrence of an anomalous nonvertical triplet energy transfer in solid conjugated polymer films is demonstrated for the first time employing the "nonvertical" COT triplet acceptor, which appears to behave similarly to conventional vertical triplet acceptors, such as anthracene. Both dopant molecules are found to efficiently quench the host phosphorescence of the polymer without affecting the host fluorescence--this can be attributed to the large singlet-triplet (S(1)-T(1)) splitting of these molecules. This S(1)-T(1) splitting is exceptionally large in COT due to its low-lying relaxed triplet state, which is capable of accepting host triplet excitations. In contrast to anthracene, the triplet lifetime of the COT molecules is reasonably short, thus making a fast deactivation of the triplet excitations possible. This suggests that nonvertical triplet scavengers might be promising candidates for quenching the host triplet excitations in future electrically pumped fluorescence organic lasers, which suffer from excessive triplet-state losses.