  In the present paper we continue the project of systematic construction of
invariant differential operators on the example of the non-compact algebras
$su(n,n)$. Earlier were given the main multiplets of indecomposable elementary
representations for $n\leq 4$, and the reduced ones for $n=2$. Here we give all
reduced multiplets containing physically relevant representations including the
minimal ones for the algebra $su(3,3)$. Due to the recently established
parabolic relations the results are valid also for the algebra
$sl(6,\mathbb{R})$ with suitably chosen maximal parabolic subalgebra.
