if it is in general OLS, R^2=1-SSreg/SSerror, then R^2 in non-linear model is not defined because SSerror in nonlinear model does not necessary mean anything. The mean of residual is not necessary zero, and the variance of residual is not constant. The totalSS not equals SSreg+SSerror any more. This is simply due to the fact that nonlinear model is not estimated by minimizing least square of residual anyway.

However, people have defined R^2 similar measures such as McFadan's likelihood ratio stuff, information reduction ratio, and so forth.

To check goodness of fit for nonlinear model, one is to use deviance difference and graphic check.