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Despite intensive efforts, the fluorescence of perovskite nanocrystals (NCs) still suffers from a poor color purity, which limits the applications in light emitting and multicolor display. A deep understanding on the fundamental of the photoluminescent (PL) spectral broadening is thus of great significance. Herein, the PL decay curves of the CsPbCl_xBr_3-x NCs are monitored at different wavelengths covering the entire PL band. Moreover, energy relaxation time τ and radiative recombination time β are obtained by numerical fittings. The dependences of τ and 1/β on the detection wavelength agree well with the steady-state PL spectrum, indicating the observed PL broadening is an intrinsic effect due to the resonance and off-resonance exciton radiative recombination processes. This work not only provides a new analysis method for time-resolved PL spectra of perovskites, but also gains a deep insight into the spectral broadening of the lead halide perovskite NCs.