Many politically and economically important groups are themselves comprised of groups. Examples of such multilevel group structures include coalition governments, labor confederations and multinational agreements. This paper develops a model of multilevel group structures. The results establish the way in which individuals and groups will make trade-offs across levels of the multilevel structure. They also establish that overall stability and overall instability can both arise from any combination of stable and unstable levels. An important conclusion is that the stability of multilevel group structures cannot generally be understood by independently analyzing the component levels as is the conventional approach to coalitional games. Implications for institutional design are also discussed, including a condition for determining when a game among groups will destabilize the groups themselves. Finally, a detailed example of a political party formation and power sharing game is analyzed in this framework.