We consider the evolution by mean curvature flow of surface clusters,
where along triple edges three surfaces are allowed to meet under an equal angle
condition. We show that any such smooth flow, which is weakly close to the static
flow consisting of three half-planes meeting along the common boundary, is smoothly
close with estimates. Furthermore, we show how this can be used to prove a smooth
short-time existence result. This is joint work with B. White.