Stationary premixed flames in dual-source flow are considered. The significant features of the dual-source system are that the sources are of finite strength, and that a stagnation point is located between the sources. A new mathematical model for front propagation and advection is introduced that tracks the front along streamlines. The equations for the stationary fronts of the dual-source system are solved numerically. The assumption of constant-density potential flow is made to simplify the problem and to illustrate the effects of the geometry alone. It is shown that for sufficiently slow burning velocity (or equivalently, small source separation), three stationary states exist for closed, free flames, but one of them is unstable. In addition, several types of burner-attached flames are observed. Quasi-stationary evolution of a closed, free flame exhibits a change of topology and hysteresis. Nonclosed flames are predicted if local extinction due to flow strain is allowed.