Most polio virus infections are silent. Vaccination reduces the incidence of infection, and the period between clinical cases of poliomyelitis becomes longer. As the point of eradication is approached, it becomes increasingly difficult to use the case-free period to determine whether silent infections have ceased. In this paper, the authors use stochastic computer simulations to relate case-free periods to the presence or absence of silent infections. After 2 years without paralytic cases in a population of 200,000 inhabitants, the probability for the presence of silent infections can still be as high as 38%. The case-free period must exceed 3 years before one can be 95% certain that there has been local extinction of the wild polio virus infection. Even after 5 years without cases, the probability of silent polio virus transmission can still be in the range of 0.1-1.0%.