  We study different conditions which turn out to be equivalent to
equicontinuity for a transitive compact Hausdorff flow with a general group
action. Among them are a notion of "regional" equicontinuity, also known as
"Furstenberg" condition, and the condition that every point of the phase space
is almost automorphic. Then we study relations on the phase space arising from
dynamical properties, among them the regionally proximal relation and two
relations introduced by Veech. We generalize Veech's results for minimal
actions of non-Abelian groups preserving a probability measure with respect to
the regionally proximal relation. We provide proofs in the framework of
dynamical systems rather than harmonic analysis as given by Veech.
