  A `persistence exponent' $\theta$ is defined for nonequilibrium critical
phenomena. It describes the probability, $p(t) \sim t^{-\theta}$, that the
global order parameter has not changed sign in the time interval $t$ following
a quench to the critical point from a disordered state. This exponent is
calculated in mean-field theory, in the $n=\infty$ limit of the $O(n)$ model,
to first order in $\epsilon = 4-d$, and for the 1-d Ising model. Numerical
results are obtained for the 2-d Ising model. We argue that $\theta$ is a new
independent exponent.
