The mode I fatigue crack propagation (FCP) response of the closed-cell aluminium alloy foams Alulight and Alporas have been measured for a relative density in the range 0.1 to 0.4. The validity of linear elastic fracture mechanics (LEFM) to characterise the fatigue crack propagation (FCP) response is demonstrated, and K-increasing and K-decreasing tests are used to determine the full shape of the FCP response. The classical sigmoidal variation of log d a/d N with log Δ K is evident, with a Paris-law exponent m=20 for Alulight and m=25 for Alporas. The effects of relative density, mean stress and a single peak overload on the FCP response are investigated. The study concludes by analysing the mechanism of fatigue crack growth; it is suggested that the fatigue crack growth rate is controlled by the progressive degradation of crack bridging by fatigue failure of the cell edges behind the crack tip.