  Two models of driven optical cavities, based on two-dimensional
Ginzburg-Landau equations, are introduced. The models include loss, the Kerr
nonlinearity, diffraction in one transverse direction, and a combination of
diffusion and dispersion in the other one (which is, actually, a temporal
direction). Each model is driven either parametrically or directly by an
external field. By means of direct simulations, stable completely localized
pulses are found (in the directly driven model, they are built on top of a
nonzero flat background). These solitary pulses correspond to spatio-temporal
solitons in the optical cavities. Basic results are presented in a compact form
as stability regions for the solitons in a full three-dimensional parameter
space of either model. The stability region is bounded by two surfaces; beyond
the left one, any two-dimensional (2D) pulse decays to zero, while quasi-1D
pulses, representing spatial solitons in the optical cavity, are found beyond
the right boundary. The spatial solitons are found to be stable both inside the
stability region of the 2D pulses (hence, bistability takes place in this
region) and beyond the right boundary of this region (although they are not
stable everywhere). Unlike the spatial solitons, their quasi-1D counterparts in
the form of purely temporal solitons are always subject to modulational
instability, which splits them into an array of 2D pulses, that further
coalesce into two final pulses. A uniform nonzero state in the parametrically
driven model is also modulationally unstable, which leads to formation of many
2D pulses that subsequently merge into few ones.
