The statistical distribution of slug lengths in a gas-liquid pipeline evolves along the pipe as short slugs collapse. This results from a lack of development of the liquid velocity profile at the rear of each slug that is shorter than a minimum stable length. Experiments have been conducted in a 50 mm diameter tube inclined at +5 degrees to the horizontal to determine the rate of collapse of short slugs as a function of their length. The data covers both stagnant and turbulent flowing liquid, in both the elongated bubble and slug flow regimes. The data shows that all the turbulent how results may be correlated by the same expression regardless of the value of the slug liquid Reynolds number. This correlation is employed within a model adapted for horizontal flow that assumes a random distribution of slug lengths at the pipe entrance and calculates the evolution of the slug length distribution along a pipe. The results of the model are compared against experimentally determined slug length distributions obtained in a 16 m long pipe. The comparison between the calculated and observed average slug length is shown to be quite good over a range of flow rates and the overall shape of the length distributions is predicted well by the model.