It is analytically shown that weak initial spectral phase modulations cause a pulse-contrast degradation at the output of nonlinear chirped-pulse amplification systems. The Kerr-nonlinearity causes an energy-transfer from the main pulse to side-pulses during nonlinear amplification. The relative intensities of these side-pulses can be described in terms of Bessel-functions. It is shown that the intensities of the pulses are dependent on the magnitude of the accumulated nonlinear phase-shift (i.e., the B-integral), the depth and period of the initial spectral phase-modulation and the slope of the linear stretching chirp. The results are applicable to any type of laser amplifier that is based on the technique of chirped-pulse amplification. The analytical results presented in this paper are of particular importance for high peak-power laser applications requiring high pulse-contrasts, e.g. high field physics.