  The explicit expression of the flow equations of the noncommutative
Kadomtsev-Petviashvili(ncKP) hierarchy is derived. Compared with the flow
equations of the KP hierarchy, our result shows that the additional terms in
the flow equations of the ncKP hierarchy indeed consist of commutators of
dynamical coordinates \{$u_i$\}. The recursion operator for the flow equations
under $n$-reduction is presented. Further, under 2-reduction, we calculate a
nonlocal recursion operator $\Phi(2)$ of the noncommutative Korteweg-de
Vries(ncKdV) hierarchy, which generates a hierarchy of local, higher-order
flows. Thus we solve the open problem proposed by P.J. Olver and V.V.
Sokolov(Commun.Math.Phys. 193 (1998), 245-268).
