We report on optically induced, ultrafast magnetization dynamics in the Heusler alloy Co 2 FeAl, probed by time-resolved magneto-optical Kerr effect. Experimental results are compared to results from electronic structure theory and atomistic spin-dynamics simulations. Experimentally, we find that the demagnetization time (τ M ) in films of Co 2 FeAl is almost independent of varying structural order, and that it is similar to that in elemental 3d ferromagnets. In contrast, the slower process of magnetization recovery, specified by τ R , is found to occur on picosecond time scales, and is demonstrated to correlate strongly with the Gilbert damping parameter (α). Our results show that Co 2 FeAl is unique, in that it is the first material that clearly demonstrates the importance of the damping parameter in the remagnetization process. Based on these results we argue that for Co 2 FeAl the remagnetization process is dominated by magnon dynamics, something which might have general applicability.