We report on the most recent results from a series of high power tests being carried out on rf-driven dielectricloaded accelerating (DLA) structures. The purpose of these tests is to determine the viability of the DLA as a traveling-wave accelerator and is a collaborative effort between Argonne National Laboratory (ANL), Naval Research Laboratory (NRL), and Stanford Linear Accelerator Center (SLAC). In this paper, we report on the recent high power tests of a fused quartz-based DLA structure that was carried out at incident powers of up to 12 MW at NRL and 37 MW at SLAC. We also report on test results of a TiN coated quartz structure, that exhibits good multipactor suppression.