  We show that Lagrangian submanifolds in six-dimensional nearly K\"ahler (non
K\"ahler) manifolds and in twistor spaces $Z\sp{4n+2}$ over quaternionic
K\"ahler manifolds $Q\sp{4n}$ are minimal. Moreover, we will prove that any
Lagrangian submanifold $L$ in a nearly K\"ahler manifold $M$ splits into a
product of two Lagrangian submanifolds for which one factor is Lagrangian in
the strict nearly K\"ahler part of $M$ and the second factor is Lagrangian in
the K\"ahler part of $M$. Using this splitting theorem we then describe
Lagrangian submanifolds in nearly K\"ahler manifolds of dimensions six, eight
and ten.
