We analyze metastability and nucleation in the context of a local version of the Kawasaki dynamics for the two-dimensional anisotropic Ising lattice gas at very low temperature. Let ??¿Z2 be a sufficiently large finite box. Particles perform simple exclusion on ??, but when they occupy neighboring sites they feel a binding energy -U1 0 is an activity parameter. Thus, the boundary of ?? plays the role of an infinite gas reservoir with density ¿. We take ??¿ (U1,U1 +U2) where the totally empty (full) configuration can be naturally associated to metastability (stability). We investigate how the transition from empty to full takes place under the dynamics. In particular, we identify the size and some characteristics of the shape of the critical droplet and the time of its creation in the limit as ß¿8. We observe very different behavior in the weakly or strongly anisotropic case. In both case we find that Wulff shape is not relevant for the nucleation pattern.