## Abstract

Let G be a complex reductive algebraic group. We construct the moduli spaces of tensor fields of special type on a large class of varieties X including seminormal varieties and varieties satisfying Serre's condition S2. We use them to construct compactified moduli spaces of principal G-bundles on X in case X is irreducible. We also give a simpler construction of the moduli spaces of orthogonal and symplectic sheaves on curves with ordinary nodes and cusps.