Dexter energy transfer (DET) of triplet electronic states is used to direct energy in photovoltaics, quench reactive singlet oxygen species in biological systems, and generate them in photodynamic therapy. However, the extent to which repeated DET between aromatic residues can lead to triplet energy migration in proteins has not been investigated. Here, we computationally describe DET rates in microtubules, actin filaments and the intermediate filament, vimentin. We discover instances where interaromatic residue Dexter couplings within individual protein subunits of these polymers are similar those of small molecules used for organic electronics. However, interaromatic residue coupling is mostly weak (<10-3 eV), limiting triplet energy diffusion lengths to 6.1, 0.5 and 1.0 Å in microtubules, actin filaments and vimentin, respectively. On the other hand, repeated förster resonance energy transfer (FRET) between aromatic residues leads to singlet energy diffusion lengths of 12.4 Å for actin filaments and about 8.6 Å for both microtubules and vimentin filaments. Our work shows that singlet energy migration dominates over triplet energy migration in cytoskeletal polymers.