Both rulings were put on hold pending appeal. In Mississippi case, the state defendants, Republican Governor Phil Bryant and Republican Attorney General Jim Hood have already filed a notice of appeal to the 5th Circuit Court of Appeals, which is already considering appeals bans on marriage equality from Texas and Louisiana. Presumably Arkansas will appeal to the 8th Circuit. All the red states which have legally enforceable bans on marriage equality to date are in either the 5th, 6th or 8th Circuits.
Hat/tip to Joe Jervis