  The aim of this paper is to give a sharp definition of Bell's notion of local
causality. To this end, first we unfold a framework, called local physical
theory, integrating probabilistic and spatiotemporal concepts. Formulating
local causality within this framework and classifying local physical theories
by whether they obey local primitive causality --- a property rendering the
dynamics of the theory causal, we then investigate what is needed for a local
physical theory, with or without local primitive causality, to be locally
causal. Finally, comparing Bell's local causality with the Common Cause
Principles and relating both to the Bell inequalities we find a nice
parallelism: Bell inequalities cannot be derived neither from local causality
nor from a common cause unless the local physical theory is classical or the
common cause is commuting, respectively.
