What are the most common causes of ataxia and hyperreflexia?

The brain. Hyperreflexia is increased reflexes. This is an "upper motor neuron" issue, and comes from diseases of the brain such as multiple sclerosis or a stroke. Cervical spine stenois (tightness) can also cause this bilaterally. Ataxia is incoordination of motor movements. Most commonly this occurs from disease of the cerebellum. These can be acquired (toxins, low b12) and genetic.