In this paper, we analyze polling systems with multiple types of simultaneous arrivals, namely, batches of customers may arrive at the different queues at an arrival epoch. We consider cyclic polling systems with Ν queues, general service time distribution in each queue and general switchover times. For both the exhaustive and the gated service disciplines we derive the necessary equations for computing the Ν expected waiting time figures. A “pseudo” conservation law for these systems is also derived. The analysis approach can be applied to other polling systems with multitype simultaneous arrivals.