(Al,In)GaN laser diodes are used as the blue and green light source in RGB laser projection, e.g. head-up displays, laser (cinema) projection, and augmented virtual reality. For these applications, a modulation frequency bandwidth in the 100 MHz to 1 GHz range is necessary. We investigate the spectral and temporal dynamics of state-of-the-art 450 nm and 530 nm (Al,In)GaN laser diodes upon modulation with single pulses and pulse patterns, with and without pre-bias, and relate the observed dynamic characteristics to the optical gain spectra. Firstly, in the few MHz range, longitudinal mode competition causes a modulation of the modes of the laser diode’s longitudinal mode frequency comb. Mode competition is caused by variation in the gain smaller than 1/cm. Direct electrical modulation of the laser diode driving current in the MHz frequency range therefore interferes with mode competition. While this is not observable in spectrally integrated time traces of the optical intensity, it does result in a MHz intensity modulation in laser projection if wavelength sensitive elements are in the light path. Secondly, turn-on delay and relaxation oscillations affect the intensity trace on the high frequency side of the modulation frequency spectrum and are caused by large > 10/cm gain variations. Pre-bias and multiple pulses with pulse spacing in the 10 ns range affect intensity of first and consecutive pulses. Furthermore, the spectro-temporal behavior shows longitudinal mode bunching, caused by irregular modulation of the wavelength dependent gain spectrum.