Social learning is the basis for the formation of traditions in both human and nonhuman animals. Field observations and experiments provide evidence for the existence of traditions in animals but they do not address the underlying social-learning mechanisms. We used an established laboratory experimental paradigm, the artificial fruit design, to test for copying of a sequence of actions and local enhancement in six groups of wild vervet monkeys, Chlorocebus aethiops. We introduced a two-step task where models had to remove a bar to untie a rope that blocked a single door of a box. The models were high-ranking individuals that monopolized the box early on and discovered by trial and error how to open it. We obtained successful models in three groups, while the other three groups acted as controls. After 20 successful demonstrations, we tested subjects with a box that had a rope in the same position but the rope was not functional. Under these conditions, sequential copying of the two-step opening did not occur. Only individuals that were exposed to models were likely to touch the bar if door opening was not immediately successful, providing evidence for local enhancement. When we presented the boxes with the functional rope, we found no effect of having been exposed to a model on the probability that subjects solved the task. We conclude that the social-learning abilities of wild vervet monkeys are relatively limited and discuss potential problems concerning the technical difficulty of the task