Can I use ANOVA if my parameters are nonlinear?

Hello,

I am working with design of experiments (full factorial designs to be precise) and I need to analyze my results now.

My goal is to find out which parameters and interactions have influence on my respons variable.

I used the anovan, but now I have a doubt if I should, because I have a nonlinear system.

So my question is, can I use it if my parameters variate nonlinearly with the response?

If not, could you recommend me another method?

Thank you, Amanda