A covariant gauge-invariant three-dimensional description of relativistic bound-states

A formalism is presented which allows covariant three-dimensional boundstate equations to be derived systematically from four-dimensional ones without the use of delta-functions. The amplitude for the interaction of a bound state described by these equations with an electromagnetic probe is constructed. This amplitude is shown to be gauge invariant if the formalism is truncated at the same coupling-constant order in both the interaction kernel of the integral equation and the electromagnetic current operator.