  We study 2-local reflexivity of the set of all surjective isometries between
certain function spaces. We do not assume linearity for isometries. We prove
that a 2-local isometry in the group of all surjective isometries on the
algebra of all continuously differentiable functions on the closed unit
interval with respect to several norms is a surjective isometry. We also prove
that a 2-local isometry in the group of all surjective isometries on the Banach
algebra of all Lipschitz functions on the closed unit interval with the
sum-norm is a surjective isometry.
