The secular evolution of barred galaxies is explored using N-body simulation and linear analysis. In particular, we examine the interaction between bars and spheroidal components of galaxies. According to our calculations, this interaction drives secular transfer of angular momentum from bars to spheroids, primarily through resonant coupling. A moderately strong bar, having mass within corotation ~0.3 times the enclosed spheroid mass, is predicted to shed all its angular momentum typically in less than ~10^9^ yr, which is quite short compared to the ages of galactic disks. Even shorter depletion time scales are found for relatively more massive bars. Given that most disk galaxies possess both bars and spheroids, our results suggest either that spheroids around barred galaxies are structured so as to inhibit strong coupling with bars, or that bars can form by unknown processes long after disks are established. Our models reinforce the notion that bars can drive secular evolution in galaxies. Back-reaction on the bar is expected to be important, and we show explicitly that the structure of spheroids can be strongly modified by accepting angular momentum from bars. At the rates predicted by our analysis, this effect spins up otherwise nonrotating spheroids causing significant flattening and produces cores in spheroids whose central densities are initially singular.