We have used a novel bolometric technique and a resonant technique to obtain accurate submillimeter and microwave residual loss data for epitaxial thin films of YBa2Cu3O7, Tl2Ca2Ba2Cu3O10, and Tl2CaBa2Cu2O8. For all films we obtain good agreement between the submillimeter and microwave data, with the residual losses in both the Y-Ba-Cu-O and Tl-Ca-Ba-Cu-O films scaling approximately as frequency squared below ∼1 THz. We are able to fit the losses in the Y-Ba-Cu-O films to a weakly coupled grain model for the a-b plane conductivity, in good agreement with results from a Kramers-Kronig analysis of the loss data. We observe strong phonon structure in the Tl-Ca-Ba-Cu-O films for frequencies between 2 and 21 THz, and are unable to fit these losses to the simple weakly coupled grain model. This is in strong contrast to the case for other high-Tc superconductors such as YBa2Cu3O7, where phonon structure observed in ceramic samples is absent in epitaxial oriented films and crystals because of the electronic screening due to the high conductivity of the a-b planes. © 1992 Plenum Publishing Corporation.