I think that if culture is defined as learned behavior, than it is reasonable to say that primates posses a form of culture. Primates have been observed making tools to aid in collecting food and developing communication system, both of which are learned behaviors.
It is common in monkeys, apes and humans that behavior and social organization aren't necessarily programmed into the genes. There have been several cases where an entire troop has learned from the experiences of just a few. In a group of Japanese macaques, for example, a three-year-old female female developed the habit of washing dirt of of sweet potatoes before she ate them. First her mother, and then peers and then the entire troop started washing their potatoes too. Another macaque troop has a similar experience when a group of dominant males learned to eat wheat. Within an hour, the practice had spread throughout the entire group. Changes in learned behavior seem to spread more quickly from the top down than from the bottom up.
For monkeys as for people, the ability to learn is a tremendous adaptive advantage, permitting them to avoid fatal mistakes. Faced with an environmental change, primates don't have to wait for a genetic or physiological response, since learned behavior and social patterns can be modified.
The extensive usage of tools among primates can also be sited as culture. Chimps have been observed crumpling up leaves to dip in water than they cannot get to with their mouth and using the leaves as sponges. This kind of practice goes beyond animal instinct.
Another highly developed practice is terminating'. Chimps carefully choose the right kind of twig to probe the termite hills with. They modify the twig by peeling off the bark to expose the sticky surface. Then they dig holes with their fingers, stick the twig in and fish around until the have enough termites on their twig to have a meal.
Terminating takes time,...