The rate of moisture transfer through a peanut oil film was measured. It was found that the rate can be expressed by the equation: r = [k a1 (Δ a)]/t where r is the rate in g water/cm2/day, a1 is the higher water activity, Δ a is the difference in the water activity across the barrier, t is the film thickness and k is a constant. This principle was extended to fat-humectant systems where the lower water activity phase is intimately distributed through the fatty medium such as peanut butter and chocolate liquor. Doubling the fat content should increase the film thickness around each particle by 2 and halve the transmission rate as was found experimentally.