Overdamped motion of Brownian particles in spatially periodic potentia
ls and subjected to fluctuations modeled by asymmetric exponentially c
orrelated two-state noise of zero mean value is considered. The probab
ility current is presented in a closed form and analyzed in asymptotic
regimes of very long and very short correlation times of the fluctuat
ions. Explicit results are obtained for a piecewise linear potential.
The role of correlations nod temporal asymmetry of fluctuations is elu
cidated.