I don't think arima works exactly the way one would expect when there is differencing. What I think should happen is that by default the mean of the differenced series is estimated and if include.mean=F, then it is not. This is not what happens. Instead when there is differencing the include.mean argument is ignored. Now I guess, someone could argue that the mean of the original series doesn't exist when using a model with differencing. In this case, then the arima function doesn't conveniently estimate models with deterministic drift like the ARIMA(0,1,1) with drift. Such models are occassionally important. As a workaround, one can do the differencing outside of arima. But I don't think things should work like that! Most other time series software doesn't do this. Ian McLeod