Many Authors have discussed Nonlinear Regression based upon the LEVENBERG-MARQUART algorithm. Often the SIGMAPLOT Program is very useful, too. In this worksheet the Maple routine NonlinearFit [Statistics] has been preferred, to fit nonlinear model functions to given data. This routine is very effective and simple to use. Examples in this document include the envelopes of FRENEL's integrals and the hardening of an aluminium alloy.