  We consider shock measures in a class of conserving stochastic particle
systems on Z. These shock measures have a product structure with a step-like
density profile and include a second class particle at the shock position. We
show for the asymmetric simple exclusion process, for the exponential
bricklayers' process, and for a generalized zero range process, that under
certain conditions these shocks, and therefore the second class particles,
perform a simple random walk. Some previous results, including random walks of
product shock measures and stationary shock measures seen from a second class
particle, are direct consequences of our more general theorem. Multiple shocks
can also be handled easily in this framework. Similar shock structure is also
found in a nonconserving model, the branching coalescing random walk, where the
role of the second class particle is played by the rightmost (or leftmost)
particle.
