In recent years, Domain Decomposition Methods (DDM) have emerged as advanced solvers in several of computational mechanics. In particular, during the last decade, in the area of solid and structural mechanics, they reached a considerable level of advancement and were shown to be more efficient than popular solvers, like advanced sparse direct solvers. The present paper explores the extent of application of the general concept of force-displacement duality in DDM. A general framework for the definition of DDM is set up and it is shown that if the definition of a DDM meets some requirements, then it can lead to one primal and one dual formulation. A number of DDM are included in this setting and particular implications for each one of them is researched.