Largely asymmetric spectra are observed for ultrashort light pulses from a synchronously and passively mode-locked CW rhodamine 6G dye laser, with relatively high intra-cavity intensity. The spectral shape shows a broad wing on the long-wavelength side alone. When the asymmetric spectrum occurs, the conventional SHG intensity auto-correlation trace shows exponential-like long tails. Further, the temporal characteristics of the mode-locked pulses, including both the shape and phase, are also examined by a new method of SHG autocorrelation, where the SH output is spectrally resolved. These experimental results are explained with self-phase modulation (SPM) process due to the optical Kerr effect in a mixed dye jet stream inside the laser cavity. The main observed characteristics are in reasonable agreement with the theoretical expectation from the slow SPM mechanism, where the pulse width is much shorter than the relaxation time τrof refractive index. The measured nonlinear refractive index n2and τralso support the above interpretation.