This paper studies whether agents must agglomerate at a single location in a class of models of two-sided interaction. In these models there is an increasing returns effect that favors agglomeration, but also a crowding or market-impact effect that makes agents prefer to be in a market with fewer agents of their own type. We show that such models do not tip in the way the term is commonly used. Instead, they have a broad plateau of equilibria with two active markets, and tipping occurs only when one market is below a critical size threshold. Our assumptions are fairly weak, and are satisfied in Krugman's [1991b] model of labor market pooling, a heterogeneous-agent version of Pagano's [1989] asset market model, and Ellison, Fudenberg and Mb̲ius's [2002] model of competing auctions. Keywords: Tipping, Agglomeration, Two-sided Markets, Network Externalities, Increasing Returns. JEL Classification: R1, G2, C7.