  Let D^r_+[0,1], r >= 1, denote the group of orientation-preserving C^r
diffeomorphisms of [0,1]. We show that any two representations of Z^2 in
D^r_+[0,1], r >= 2, are connected by a continuous path of representations of
Z^2 in D^1_+[0,1]. We derive this result from the classical works by G.
Szekeres and N. Kopell on the C^1 centralizers of the diffeomorphisms of [0,1)
which are at least C^2 and fix only 0.
