  A well-known result by L. Markus, later extended by D. A. Neumann, states
that two continuous flows on a surface are equivalent if and only if there is a
surface homeomorphism preserving orbits and time directions of their separatrix
configurations.
  In this paper we present several examples showing that, as originally
formulated, the Markus-Neumann theorem needs not work. Besides, we point out
the gap in its proof and show how to restate it in a correct (and slightly more
general) way.
