[heavyset_go]

Reflexes do not necessarily have to exist in the brain, but they do exist in the central nervous system. The peripheral nervous system doesn't handle reflexes as far as I'm aware.

[johnisgood]

PNS does not process reflexes, but it is essential for transmitting the sensory and motor components of reflex arcs though.

But yeah, reflexes are processed in the central nervous system (CNS), typically the spinal cord or brainstem, not necessarily the brain.