Laminar triple flames are investigated numerically by using detailed and reduced chemical reaction mechanisms. Triple flames are believed to play an essential role in flame propagation in partially premixed systems. In order to reduce the computational cost of the simulations, the flamelet-generated manifold (FGM) method is used to simplify the chemistry model. The FGM method is based on a library of premixed laminar flamelets. Mixture fraction variations in partially premixed flames are taken into account by using the mixture fraction as an extra degree of freedom. A comparison of the results computed with FGM and with detailed chemistry shows that FGM predicts the structure of triple flames very accurately.The gradient of the mixture fraction in the unburnt mixture is varied and its influence on the structure and propagation of triple flames is studied. For decreasing gradients the curvature of the premixed flame branch decreases and the propagation velocity increases. Due to the diffusive nature of the flow and the use of symmetry boundary conditions in lateral direction, high mixture fraction gradients could not be realized at the position of the flame. As a result the trailing diffusion flame branch is only weakly present. The heat release in the premixed flame branches is two orders of magnitude higher than in the diffusion flame branch. The premixed and diffusion flame branches are studied by using a flamelet analysis. Flame stretch and curvature appear to be significant in the premixed flame branch of a triple flame. These effects cause a decrease of the local mass burning rate of almost 15%. The structure of the diffusion flame branch appears to be similar to the structure of a counterflow diffusion flame with the same scalar dissipation rate.