  We study the stochastic dynamics of coupled states with transition
probabilities depending on local persistence, this is, the time since a state
has changed. When the population has a preference to adopt older states the
system orders quickly due to the dominance of the old state. When preference
for new states prevails, the system can show coexistence of states or
synchronized collective behavior resulting in long ordering times. In this
case, the magnetization $m(t)$ of the system oscillates around $m(t)=0$.
Implications for social systems are discussed.
