A dynamic model of the asymmetric Ising glass is presented: an Ising model with antiferromagnet bonds with probabilities q arranged at random in a ferromagnetic matrix. The dynamics is introduced by changing the arrangement of the antiferromagnetic bonds after n Monte Carlo steps but keeping the same value of q and spin configuration. In the region where there is a second order transition between the ferromagnetic and paramagnetic states the dynamic behaviour follows that expected for motional narrowing and reverts to the static behaviour only for large n. There is a different dynamic behaviour where there is a first order transition between the ferromagnetic and spin glass states where it shows no effects of motional narrowing. The implications of this are discussed. This model is devised to explain the properties of doped ZnO where the magnetisation is reduced when the exchange interactions change with time. ; Comment: Paper was presented at MMM 2008 and is accepted for publication in J.A.P