We report very pronounced line asymmetries during a long duration flare on the dM6 star LHS 2034 (AZ Cnc). While all lines of the Balmer series and all strong He i lines show these asymmetries, the metal lines do not. This can be explained with the help of PHOENIX model chromospheres considering the formation depth of the lines involved. Moreover, the asymmetries persist over about one hour changing shape and amplitude. Fitting the asymmetries with an additional broad Gaussian component leads us to the scenario of a series of downward propagating condensations that decelerate due to the higher density of the lower chromosphere. In addition, similar but weaker line asymmetries were found in LHS 2397a.