Well one neurological cause of stuttering is stroke. Some stroke victims have been known to start stuttering. Another is a head injury. Depending on what brain area is damaged, that person can develop a stammer. Another is genetic. It's known that it's common for it to run in families. And researches how found this gene in humans and in song birds. So its possible this gene influences neurological development of speech areas in the brain like brocas and wernikes area to develop certain deficits.