  This paper deals with the boundary behavior of functions in the de
Branges--Rovnyak spaces. First, we give a criterion for the existence of radial
limits for the derivatives of functions in the de Branges--Rovnyak spaces. This
criterion generalizes a result of Ahern-Clark. Then we prove that the
continuity of all functions in a de Branges--Rovnyak space on an open arc $I$
of the boundary is enough to ensure the analyticity of these functions on $I$.
We use this property in a question related to Bernstein's inequality.
