Maximum likelihood estimation is a popular parameter estimation procedure however parameters may not be estimable in closed form. In this work, the maximum likelihood estimates from different distributions were obtained after the failure of the likelihood approach. The targeted models are Non Linear models with an application to a Logistic regression model. Although, obtaining the estimate of parameters for non linear models cannot be easily obtained directly. That is the solution is intractable. So there is a need to look else where, so as to obtain the solutions . In this work, R statistical package was used in performing the analysis. The result shows that convergence was attained at the 18th iteration out of 21. This also provides the values and the maximum estimate for β0 and β1.