  Target space duality is one of the most profound properties of string theory.
However it customarily requires that the background fields satisfy certain
invariance conditions in order to perform it consistently; for instance the
vector fields along the directions that T-duality is performed have to generate
isometries. In the present paper we examine in detail the possibility to
perform T-duality along non-isometric directions. In particular, based on a
recent work of Kotov and Strobl, we study gauged 2D sigma models where gauge
invariance for an extended set of gauge transformations imposes weaker
constraints than in the standard case, notably the corresponding vector fields
are not Killing. This formulation enables us to follow a procedure analogous to
the derivation of the Buscher rules and obtain two dual models, by integrating
out once the Lagrange multipliers and once the gauge fields. We show that this
construction indeed works in non-trivial cases by examining an explicit class
of examples based on step 2 nilmanifolds.
