Metamorphic proteins such as lymphotactin are a notable exception of the empirical principle that structured natural proteins possess a unique three-dimensional structure. In particular, the human chemokine lymphotactin protein exists in two distinct conformations (one monomeric and one dimeric) under physiological conditions. In this work, we use a C(alpha) Go model to show how this very peculiar behavior can be reproduced. From the study of the thermodynamics and of the kinetics, we characterize the interconversion mechanism. In particular, this takes place through the docking of the two chains living in a third monomeric, partially unfolded, state which shows a residual structure involving a set of local contacts common to the two native conformations. The main feature of two fold proteins appears to be the sharing of a common set of local contacts between the two distinct folds as confirmed by the study of two designed two fold proteins. Metamorphic proteins may be more common than expected.