  We study the structure of Wick homogenenous ideals of higher degrees in
quadratic algebras allowing Wick ordering. We present a method how to construct
a homogeneous Wick ideal $\mathcal{I}_{n+1}$ of degree $n+1$ out of a
homogeneous Wick ideal $\mathcal{I}_n$ of degree $n$ so that
$\mathcal{I}_{n+1}\subset\mathcal{I}_n$. We show that in some particular cases
our procedure allows one to get a description of the largest homogeneous Wick
ideals of higher degrees having generators of the largest quadratic Wick ideal
only. Finally we study classes of $*$-representations of Wick version of CCR
annihilating certain homogeneous Wick ideals of degree higher than $2$.
