  In this paper, we introduce the notion of a weak $(p,k)$-Dirac structure in
$TM\oplus \Lambda^pT^*M$, where $0\leq k \leq p-1$. The weak $(p,k)$-Lagrangian
condition has more informations than the $(p,k)$-Lagrangian condition and
contains the $(p,k)$-Lagrangian condition. The weak $(p,0)$-Dirac structures
are exactly the higher Dirac structures of order p introduced by N. Martinez
Alba and H. Bursztyn in [23] and [6], respectively. The regular weak
$(p,p-1)$-Dirac structure together with $(p,p-1)$-Lagrangian subspace at each
point $m\in M$ have the multisymplectic foliation. Finally, we introduce the
notion of weak $(p,k)$-Dirac morphism. We give the condition that a weak
$(p,k)$-Dirac manifold is also a weak $(p,k)$-Dirac manifold after pulling
back.
