  This article is a continuation of earlier work [R.L. Huang and Y.H. Ye, On
the second boundary value problem for a class of fully nonlinear flows I, to
appear in International Mathematics Research Notices], where the long time
existence and convergence were given on some general parabolic type special
Lagrangian equations. The long time existence and convergence of the flow had
been obtained in all cases. In particular, we can prescribe the second boundary
value problems for a family of special Lagrangian graphs.
