It is shown that viscous liquid film flow (VLF-flow) on the surfaces of slopes of martian dunes can be a low-temperature rheological phenomenon active today on high latitudes. A quantitative model indicates that the VLF-flows are consistent with the flow of liquid brines similar to that observed by imaging at the Phoenix landing site. VLF-flows depend on the viscosity, dynamics, and energetics of temporary darkened liquid brines. The darkening of the flowing brine is possibly, at least partially, attributed to non-volatile ingredients of the liquid brines. Evidence of previous VLF-flows can also be seen on the dunes, suggesting that it is an ongoing process that also occurred in the recent past.