  Let (A_0,A_1) and (B_0,B_1) be Banach couples with A_0 contained in A_1 and
B_0 contained in B_1. Let T:A_1 --> B_1 be a possibly nonlinear operator which
is a compact Lipschitz map of A_j into B_j for j=0,1. It is known that T maps
the Lions-Peetre space (A_0,A_1)_\theta,q boundedly into (B_0,B_1)_\theta,q for
each \theta in (0,1) and each q in [1,\infty), and that this map is also
compact if if T is linear. We present examples which show that in general the
map T:(A_0,A_1)_\theta,q --> (B_0,B_1)_\theta,q is not compact.
