In this work. a model is developed to treat threading dislocation (TD) reduction in (0 0 0 1) wurtzite epitaxial GaN thin films. The model is based on an approach originally proposed for (0 0 1) FCC thin film growth and uses the concepts of mutual TD motion and reactions. We show that the experimentally observed slow TD reduction in GaN can be explained by low TD reaction probabilities due to TD line directions practically normal to the film surface. The behavior of screw dislocations in III-nitride films is considered and is found to strongly impact TD reduction. Dislocation reduction data in hydride vapor phase epitaxy (HVPE) grown GaN are well described by this model. The model provides an explanation for the non-saturating TD density in thick GaN films.