The chromospheric line profile asymmetries of the flaring chromosphere can provide important diagnostics on the properties and dynamics of the flaring plasma. We study the evolution of Halpha and Ca II 8542 Å lines using unprecedented high spatio-temporal and spectral resolution ground-based observations of an M1.1 flare obtained with the Swedish Solar Telescope. The temporal evolution of the Halpha line profiles show excess emission in the red wing (red asymmetry) in the early phase of flare along a substantial part of the ribbon and excess emission in the blue wing (blue asymmetry) after the flare maximum. The Ca II 8542 Å line does not follow the same pattern. We use RADYN simulations to synthesise spectral line profiles and find good agreement with the observations. We conclude that the complex Halpha asymmetries are produced by steep velocity gradients and opacity effects.