  We show that if the gradient of $f:\RR^2\rightarrow\RR$ exists everywhere and
is nowhere zero, then in a neighbourhood of each of its points the level set
$\{x\in\RR^2:f(x)=c\}$ is homeomorphic either to an open interval or to the
union of finitely many open segments passing through a point. The second case
holds only at the points of a discrete set. We also investigate the global
structure of the level sets.
