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Given the implicit equation $F(x,y,t,s)$ of a family of algebraic planecurves depending on the parameters $t,s$, we provide an algorithm for studyingthe topology types arising in the family. For this purpose, the algorithmcomputes a finite partition of the parameter space so that the topology type ofthe family stays invariant over each element of the partition. The ideascontained in the paper can be seen as a generalization of the ideas in\cite{JGRS}, where the problem is solved for families of algebraic curvesdepending on one parameter, to the two-parameters case.

Analyzing the Topology Types arising in a Family of Algebraic Curves Depending On Two Parameters