  A hypergraph $\mathcal H$ is super-pancyclic if for each $A \subseteq
V(\mathcal H)$ with $|A| \geq 3$, $\mathcal H$ contains a Berge cycle with base
vertex set $A$. We present two natural necessary conditions for a hypergraph to
be super-pancyclic, and show that in several classes of hypergraphs these
necessary conditions are also sufficient for this. In particular, they are
sufficient for every hypergraph $\mathcal H$ with $ \delta(\mathcal H)\geq
\max\{|V(\mathcal H)|, \frac{|E(\mathcal H)|+10}{4}\}$.
  We also consider super-cyclic bipartite graphs: those are $(X,Y)$-bigraphs
$G$ such that for each $A \subseteq X$ with $|A| \geq 3$, $G$ has a cycle $C_A$
such that $V(C_A)\cap X=A$. Such graphs are incidence graphs of super-pancyclic
hypergraphs, and our proofs use the language of such graphs.
