working in a path integral in terms of the component fields. The dependences of the Liouville mode in the anomalies were directly calculated while the dependences of the Liouville superpartners were determined by using the global supersymmetry . The final results were written in terms of superfields.

The effective $N=2$ super-Liouville theory was constructed at one loop level and there is a finite renormalization of the coupling constant, i.e., from $2-d$ to $1-d$. The algebra of the operators in  gives rise to an $N=2$ superfield extension of the topological conformal algebra for any value of dimensions $d$ without any anomalous terms. The crucial points for this property are the vanishing of the ghost number anomaly and the definition of the BRST supercurrent. Our observation shows an appearing of a quite simplification in the $N=2$ case and also suggests a topological nature of the $N=2$ super-Liouville theory.

The $N=2$ critical string can be considered as an $N=2$ subcritical string in dimension $1$ plus the Liouville superfield. All the above features distinguish $N=2$ string from the $N=0$ and $N=1$ strings. The physical relevance of the topological algebra is under study.

Let us recall some basic facts of $N=2$ string in the superfield 