In this work we obtain a classification of rank two p-local finite groups for an odd prime p. This classification complements the classical result for finite simple groups of 2-rank two, and it is obtained, in view of Alperin's 3 Fusion Theorem for p-local finite groups, by means of an analysis of the outer automorphisms groups of the possible proper F-radical subgroups. New families of resistant groups, the analog concept to the group theoretical concept of Swan group, and new exotic 3-local finite groups are found.