Let \(M_ 0G\) be the identity component of the group of smooth maps from a compact manifold X to a compact simple Lie group G. The diffeomorphisms of X act as automorphisms of \(M_ 0G\); another obvious class of automorphisms of \(M_ 0G\) is given by the smooth maps \(X\to Aut(G)\). The main result of this paper is that every automorphism of \(M_ 0G\), as an abstract group, is a product of automorphisms of these two types. In the course of the proof, it is also shown that every maximal normal subgroup of \(M_ 0G\) is of the form \(\{f\in M_ 0G\); \(f(x)=1\}\), for some \(x\in X\). These results were proved, under extra smoothness assumptions, in [\textit{A. N. Pressley} and \textit{G. B. Segal}, Loop Groups (Oxf. Univ. Press, 1986; Zbl 0618.22011).