  We study invariant submanifolds of manifolds endowed with a normal or complex
metric contact pair with decomposable endomorphism field $\phi$. For the normal
case, we prove that a $\phi$-invariant submanifold tangent to a Reeb vector
field and orthogonal to the other one is minimal. For a $\phi$-invariant
submanifold $N$ everywhere transverse to both the Reeb vector fields but not
orthogonal to them, we prove that it is minimal if and only if the angle
between the tangential component $\xi$ (with respect to $N$) of a Reeb vector
field and the Reeb vector field itself is constant along the integral curves of
$\xi$. For the complex case (when just one of the two natural almost complex
structures is supposed to be integrable), we prove that a complex submanifold
is minimal if and only if it is tangent to both the Reeb vector fields.
