We investigated the interaction of recombination and selection on the process of fixation of two linked loci with epistatic interactions in fitness. We consider both the probability of fixation of newly arising mutants (the static model) and the time to fixation under continued mutation (the dynamic model). Our results show that the fixation of a new advantageous combination is facilitated by higher fitness of the advantageous genotype and by weaker selection against the intermediate deleterious genotypes. Fixation occurs more rapidly when the recombination rates are small, except when selection against intermediate genotypes is weak and selection in favour of the double mutant is very strong. In these cases fixation is more rapid when the recombinant rate is large. Mutations of strong effects, deleterious when alone but beneficial when coupled, are fixed more easily than mutations of intermediate effects, at least for large recombination rates. Among the possible pathways the process of fixation might follow, independent substitutions lead to the fixation of the double mutant only when selection is weak. The relative importance of the other pathways depends on the interaction between recombination and selection. The coupled-gamete pathway (i.e. when the population waits until the double mutant appears and then drives it to fixation) is more important as selection intensity increases and the recombination rate is reduced. For all recombination rates, asymmetries in fitness of the intermediate genotypes increase the rate at which fixations occur. Finally, throughout the fixation process, the population will be monomorphic at least at one of the two loci for most of the time, which implies that there would be little opportunity to detect the presence of negative epistasis even if it were important for occasional evolutionary transitions.