Abstract A simple mechanism for allocating indivisible resources is sequential allocation in which agents take turns to pick items. We focus on possible and necessary allocation problems, checking whether allocations of a given form occur in some or all mechanisms for several commonly used classes of sequential allocation mechanisms. In particular, we consider whether a given agent receives a given item, a set of items, or a subset of items for natural classes of sequential allocation mechanisms: balanced, recursively balanced, balanced alternation, and strict alternation. We present characterizations of the allocations that result respectively from the classes, which extend the well-known characterization by Brams and King [2005] for policies without restrictions. In addition, we examine the computational complexity of possible and necessary allocation problems for these classes.