  The geodesic complexity of a metric space X is the smallest k for which there
is a partition of X x X into ENRs E_0,...,E_k on each of which there is a
continuous choice of minimal geodesic sigma(x_0,x_1) from x_0 to x_1. We prove
that the geodesic complexity of an n-dimensional Klein bottle equals 2n. Its
topological complexity remains unknown for n>2.
