  We consider three-dimensional fermionic band theories that exhibit Weyl nodal
surfaces defined as two-band degeneracies that form closed surfaces in the
Brillouin zone. We demonstrate that topology ensures robustness of these
objects under small perturbations of a Hamiltonian. This topological robustness
is illustrated in several four-band models that exhibit nodal surfaces
protected by unitary or anti-unitary symmetries. Surface states and
Nielsen-Ninomiya doubling of nodal surfaces are also investigated.
