We present a broadband (460 - 980 nm) analysis of the nonlinear absorption processes in bulk ZnO, a large-bandgap material with potential blue-to-UV photonic device applications. Using an optical parametric amplifier we generated tunable 1-kHz repetition rate laser pulses and employed the Z-scan technique to investigate the nonlinear absorption spectrum of ZnO. For excitation wavelengths below 500 nm, we observed reverse saturable absorption due to one-photon excitation of the sample, agreeing with rate-equation modeling. Two- and three-photon absorption were observed from 540 to 980 nm. We also determined the spectral regions exhibiting mixture of nonlinear absorption mechanisms, which were confirmed by photoluminescence measurements.