  We investigate quasilocal horizons in inhomogeneous cosmological models,
specifically concentrating on the notion of a trapping horizon defined by
Hayward as a hypersurface foliated by marginally trapped surfaces. We calculate
and analyse these quasilocally defined horizons in two dynamical spacetimes
used as inhomogeneous cosmological models with perfect fluid source of non-zero
pressure. In the spherically symmetric Lema\^{i}tre spacetime we discover that
the horizons (future and past) are both null hypersurfaces provided that the
Misner-Sharp mass is constant along the horizons. Under the same assumption we
come to the conclusion that the matter on the horizons is of special characte -
a perfect fluid with negative pressure. We also find out that they have locally
the same geometry as the horizons in the Lema\^{i}tre-Tolman-Bondi spacetime.
We then study the Szekeres-Szafron spacetime with no symmetries, particularly
its subfamily with $\beta_{,z}\neq 0$, and we find conditions on the horizon
existence in a general spacetime as well as in certain special cases.
