Abstract
"T-fold" backgrounds are generically-nongeometric compactifications of string theory, described by T-n fibrations over a base N with transition functions in the perturbative T-duality group. We review Hull's doubled torus formalism, which geometrizes these backgrounds, and use the formalism to constrain the D-brane spectrum (to leading order in g(s) and alpha') on T-n fibrations over S-1 with O(n, n; Z) monodromy. We also discuss the (approximate) moduli space of such branes and argue that it is always geometric. For a D-brane located at a point on the base N, the classical "D-geometry" is a T-n fibration over a multiple cover of N.