All previous works on single-buffer polling systems assume a nonzero time for a server to switch stations. In this paper, we consider similar systems with zero switchover times. The performance measures in symmetric systems of this type correspond to those in a well-known machine interference problem. Assuming that the stochastic characteristics vary from station to station, we provide an analysis of imbedded Markov chains to calculate the performance measures. In particular, we derive the state transition probabilities for systems with an arbitrary number of stations. Our approach is also applied to non-preemptive priority systems and systems with a mixture of polling and priority scheduling. Furthermore, we obtain the Laplace-Stieltjes transforms of the probability distribution function of waiting time for both polling and priority systems. © 1990.