The motion of a triple junction is investigated. We consider only the two-dimensional case and assume that initially the fluid is in the form of three inviscid wedges. A similarity solution is determined which accounts for a balance of force at the triple junction. This similarity solution is computed numerically using boundary integral methods. Results are presented for different initial wedge angles and surface tension ratios. In particular the location of the triple junction and the resulting capillary waves along the interfaces are discussed.