  We prove that a maximal totally complex submanifold $N^{2n}$ of the
quaternionic projective space $\mathbb{H}\mathbb{P}^n$ ($n\geq 2$) is a
parallel submanifold, provided one of the following conditions is satisfied:
(1) $N$ is the orbit of a compact Lie group of isometries, (2) the restricted
normal holonomy is a proper subgroup of ${\rm U}(n)$.
