In [2], Alpay and Ercan characterized order continuous duals of spaces CD0(K, E) and CDw(K, E) where K is a compact Hausdorff space without isolated points and E is a Banach lattice. In this note, we generalize their results to an arbitrary Dedekind complete Banach lattice F, that is to say, we characterize order continuous operators on these spaces taking values in an arbitrary Dedekind complete Banach lattice F.Recall that a topological space is called basically disconnected if the closure of any Fσ -open set is open. A compact Hausdorff space that is basically disconnected will be referred to as a quasi-Stonean space. For a quasi-Stonean space K without isolated points, the following function spaces were introduced by Abramovichand Wickstead [1