We have investigated the nonlinear optical response of low loss Si(0.6)Ge(0.4) / Si waveguides in the mid-infrared wavelength range from 3.25- 4.75μm using picosecond optical pulses. We observed and measured the three and four-photon absorption coefficients as well as the Kerr nonlinear refractive index. The dynamics of the spectral broadening suggests that, in addition to multiphoton absorption, the corresponding higher order nonlinear refractive phenomena also needs to be included when high optical pulse intensities are used at mid-infrared wavelengths in this material.