  We study several properties of equi-Baire 1 families of functions between
metric spaces. We consider the related equi-Lebesgue property for such
families. We examine the behaviour of equi-Baire 1 and equi-Lebesgue families
with respect to pointwise and uniform convergence. In particular, we obtain a
criterion for a choice of a uniformly convergent subsequence from a sequence of
functions that form an equi-Baire 1 family, which solves a problem posed in
[3]. Finally, we discuss the notion of equi-cliquishness and relations between
equi-Baire 1 families and sets of equi-continuity points.
