In the paper, we consider a polling system with a cyclic adaptive polling order with exhaustive service policy. The server polls the queues in a cyclic way but skips (does not visit) those that were empty when polling them in the previous cycle. We apply the generating function method to derive first and second order moments of the stationary state distribution of the queue length at the polling moments that allows calculating the mean delay in queues. The application of the polling system is given in many areas. We provide one of applications of polling systems.