Virasoro algebras with central chargec>1

We provide evidence for a new unitary series of conformal field theories, labeled by integers M and N. For N=1,2 they reproduce the unitary conformal and superconformal series of minimal models. For higher N, they correspond to models with c>1, generated by new nonlocal currents of spin (N+4)/(N+2). We use a generalization of the Feigin-Fuchs construction to find the currents and the primary fields of the new algebras.