Using a free-electron laser source,we have studied the nonlinear absorption in I nSb,Hg1-xCdxTe and InAs semiconductors.By measuring the tr ansmission,two -photon-absorption(TPA)has been investigated as a function of the input power.In two cases,a distinct saturation of TPA coefficients has been observed.Using an extension of these methods,we demonstrated that the reduced transmission at high intensities is primarily due to free-carrier-absorption(FCA) of the electrons a nd holes generated by TPA,not directly due to the TPA process.Furthermore,by car eful calculation,we have extracted the convincing cross section of FCA.