We construct a family of non-weight modules over the super-Virasoro algebras and the $N=2$ superconformal algebras. These modules when regarded as modules over the Cartan subalgebra $\mathfrak{h}$ (modulo the center) are free of rank 1 or 2. We obtain a sufficient and necessary condition for such modules to be simple. Moreover, we determine the isomorphism classes of these modules. Finally, we show that these modules constitute a complete classification of $U(\mathfrak{h})$-free modules of rank 1 or 2. A relationship among such non-weight modules over these superalgebras is precisely presented. This is a joint work with Hengyun Yang and Limeng Xia.

会议密码:1015