Per the Rule Book, there are three Special Conditions that are marked by turning the Pokemon: Asleep, Paralyzed. and Confused. Since you can only turn a Pokemon in one direction at a time, these three will replace each other.
Burned and Poisoned, however, are marked by putting counters on the Pokemon. You can put one or two counters on a Pokemon while it is turned, so they don't replace any other special condition.