We have developed a low cost apparatus for open- and closed-aperture Z-scan measurements of multi-photon absorption (MPA) cross-sections of solid and liquid samples. The experimental setup uses simple diodes for light detection. The signals are recorded with a low-cost two-channel PC-scope. We have developed a LabView based software, which analyzes single laser pulses and allows averaging over several shots. First measurements on a CR-39 polymer demonstrated the functioning of the method. Furthermore, we have shown that for 25fsec ultra short pulses three-photon absorption (ThPa) must be considered in addition to two-photon absorption (TPA). The appropriate nonlinear absorption (TPA-, ThPA-) coefficients and the nonlinear refractive index can be obtained via a best fit of the data to theoretical curves, which have been derived and adapted for ThPA from formulas for TPA accessible in the literature.