  Surfaces admitting flows all whose orbits are dense are called minimal.
Minimal orientable surfaces were characterized by J.C. Beni\`{e}re in 1998,
leaving open the nonorientable case. This paper fills this gap providing a
characterization of minimal nonorientable surfaces of finite genus. We also
construct an example of a minimal nonorientable surface with infinite genus and
conjecture that any nonorientable surface without combinatorial boundary is
minimal.
