  We work in both the complex and in the para-complex categories and examine
(para)-K\"ahler Weyl structures in both the geometric and in the algebraic
settings. The higher dimensional setting is quite restrictive. We show that any
(para)-Kaehler Weyl algebraic curvature tensor is in fact Riemannian in
dimension at least 6; this yields as a geometric consequence that any
(para)-Kaehler Weyl geometric structure is trivial if the dimension is at least
6. By contrast, the 4 dimensional setting is, as always, rather special as it
turns out that there are (para)-Kaehler Weyl algebraic curvature tensors which
are not Riemannian in dimension 4. Since every (para)-Kaehler Weyl algebraic
curvature tensor is geometrically realizable and since every 4 dimensional
Hermitian manifold admits a unique (para)-Kaehler Weyl structure, there are
also non-trivial 4 dimensional Hermitian (para)-Kaehler Weyl manifolds.
