  We introduce partial duality of hypermaps, which include the classical
Euler-Poincar\'e duality as a particular case. Combinatorially, hypermaps may
be described in one of three ways: as three involutions on the set of flags
(bi-rotation system or $\tau$-model), or as three permutations on the set of
half-edges (rotation system or $\sigma$-model in orientable case), or as edge
3-coloured graphs. We express partial duality in each of these models. We give
a formula for the genus change under partial duality.
