  The problem of classification of connected holonomy groups (equivalently of
holonomy algebras) for pseudo-Riemannian manifolds is open. The classification
of Riemannian holonomy algebras is a classical result. The classification of
Lorentzian holonomy algebras was obtained recently.
  In the present paper weakly-irreducible not irreducible subalgebras of
$\su(1,n+1)$ ($n\geq 0$) are classified. Weakly-irreducible not irreducible
holonomy algebras of pseudo-K\"ahlerian and special pseudo-K\"ahlerian
manifolds are classified. An example of metric for each possible holonomy
algebra is given. This gives the classification of holonomy algebras for
pseudo-K\"ahlerian manifolds of index 2.
  Finally we consider some examples and applications. We describe examples of
4-dimensional Lie groups with left-invariant pseudo-K\"ahlerian metrics and
determine their holonomy algebras. We use our classification of holonomy
algebras to give a new proof for the classification of simply connected
pseudo-K\"ahlerian symmetric spaces of index 2 with weakly-irreducible not
irreducible holonomy algebras. We consider time-like cones over Lorentzian
Sasaki manifolds. These cones are also pseudo-K\"ahlerian manifolds of index 2.
We describe the local DeRham-Wu decomposition of the cone in terms of the
initial Lorentzian Sasaki manifold and we describe all possible
weakly-irreducible not irreducible holonomy algebras of such cones.
