We present the magnetisation reversal dynamics of epitaxial Fe thin films grown on GaAs(001) and InAs(001) studied as a function of field sweep rate in the range 0.01-160 kOe/s using magneto-optic Kerr effect (MOKE). For 55 and 250 Å Fe/GaAs(001), we find that the hysteresis loop area A follows the scaling relation A ∝ H^α with α=0.03~0.05 at low sweep rates and 0.33~0.40 at high sweep rates. For the 150 Å Fe/InAs(001) film, α is found to be ~0.02 at low sweep rates and ~0.17 at high sweep rates. The differing values of α are attributed to a change of the magnetisation reversal process with increasing sweep rate. Domain wall motion dominates the magnetisation reversal at low sweep rates, but becomes less significant with increasing sweep rate. At high sweep rates, the variation of the dynamic coercivity H_c is attributed to domain nucleation dominating the reversal process. The results of magnetic relaxation studies for easy-axis reversal are consistent with the sweeping of one or more walls through the entire probed region (~100 µm). Domain images obtained by scanning Kerr microscopy during the easy cubic axis reversal process reveal large area domains separated by zigzag walls.