For smooth knottings of compact (not necessarily orientable) n-dimensional manifolds in ${ℝ}^{n+2}$ (or ${}^{n+2}$), we generalize the notion of knot moves to higher dimensions. This reproves and generalizes the Reidemeister moves of classical knot theory. We show that for any dimension there is a finite set of elementary isotopies, called moves, so that any isotopy is equivalent to a finite sequence of these moves.