  Concurrent strategies based on event structures are examined from the
viewpoint of 'may' and 'must' testing in traditional process calculi. In their
pure form concurrent strategies fail to expose the deadlocks and divergences
that can arise in their composition. This motivates an extension of the
bicategory of concurrent strategies to treat the 'may' and 'must' behaviour of
strategies under testing. One extension adjoins neutral moves to strategies but
in so doing loses identities w.r.t. composition. This in turn motivates another
extension in which concurrent strategies are accompanied by stopping
configurations; the ensuing stopping strategies inherit the structure of a
bicategory from that of strategies. The technical developments converge in
providing characterisations of the 'may' and 'must' equivalences and preorders
on strategies.
