A novel theoretical approach for the description of pattern formation by adsorbates with strong lateral interactions, giving rise to a first-order phase transition, is presented. It is based on a continuum mean-field approximation and includes adsorption, desorption as well as surface migration steps, while pairwise interactions are introduced through their strength and effective radius. First applications concern the profiles of interfaces separating domains with differing coverages. Further extension to reacting systems is straightforward. The formation of ordered configurations of adsorbed particles on periodic (i.e. single crystal) substrate surfaces as a consequence of the existence of mutual interactions is more the rule than the exception and has been verified experimentally in numerous cases. Strong attractive interactions lead to the formation of patches and the separation of two phases with differing coverages characteristic of first-order phase transitions. While the global equilibrium properties of such systems as, for example, reflected by adsorption isotherms have been treated extensively in the past [II, the description of transient effects associated with local pattern formation is, to our knowledge, still largely missing, while these have now become accessible to direct experimental observation by applying scanning tunneling microscopy @TM) or related techniques.