  We present Chandra observations of a small sample of nearby classical double
radio galaxies which have more than one radio hotspot in at least one of their
lobes. The X-ray emission from the hotspots of these comparatively low-power
objects is expected to be synchrotron in origin, and therefore to provide
information about the locations of high-energy particle acceleration. In some
models of the relationship between the jet and hotspot the hotspots that are
not the current jet termination point should be detached from the energy supply
from the active nucleus and therefore not capable of accelerating particles to
high energies. We find that in fact some secondary hotspots are X-ray sources,
and thus probably locations for high-energy particle acceleration after the
initial jet termination shock. In detail, though, we show that the spatial
structures seen in X-ray are not consistent with naive expectations from a
simple shock model: the current locations of the acceleration of the
highest-energy observable particles in powerful radio galaxies need not be
coincident with the peaks of radio or even optical emission.
