  In this note we generalize an extension theorem in [5] and [9] of the mean
curvature flow to the H^{k} mean curvature flow under some extra conditions.
The main difficult problem in proving the extension theorem is to find a
suitable version of Michael-Simon inequality for the H^{k} mean curvature flow,
and to do a suitable Moser iteration process. These two problems are overcame
by imposing some extra conditions which may be weakened or removed in our
forthcoming paper [7]. On the other hand, we derive some estimates for the
generalized mean curvature flow, which have their own interesting.
