Abstract: We introduce four families of nonunitary coset conformal field theories which generalize the Wess-Zumino-Witten models on the supergroups $\mathrm{PSU}(n|n)$ and $\mathrm{OSP}(2n+2|2n)$. We show that these coset theories admit perturbations which are marginal at 2 loops and we argue in favor of their exact marginality. Finally, we discuss the implications of our findings for the sigma models on symmetric superspaces, affine Toda and Gross-Neveu models which are believed to arise as certain limits of the coset theories.