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We study business cycle fluctuations in heterogeneous-agent general equilibrium models that feature both intensive and extensive margins of labor supply. A nonconvexity in the mapping between time devoted to work and labor services combined with idiosyncratic shocks generates operative extensive and intensive margins. We consider calibrated versions of this model that differ in the value of a key preference parameter for labor supply and the extent of heterogeneity. The model is able to capture the salient features of the empirical distribution of hours worked, including how individuals transit within this distribution. We then study how the various specifications influence labor supply responses to aggregate technology shocks. We ask to what extent our predictions for business cycle fluctuations are affected by abstracting from the intensive margin and instead assuming that adjustment occurs only along the extensive margin. We find that abstracting from intensive margin adjustment can have large effects on the volatility of aggregate hours even if fluctuations along the intensive margin are small.