This paper replaces increasing product variety with quality upgrading in the Romer (1990) model. We show that the range of parameters for which a steady state exists can be divided into two subspaces with well-behaved comparative statics and saddle-point dynamics in one subspace, but with “perverse” comparative-statics properties and either equilibrium indeterminacy or instability in the other subspace. In the latter subspace, a parameter change possibly leads to a Hopf bifurcation. Using a theorem in Arnold (in press), these results for the closed economy can also be used to characterize the dynamics of the M-country open-economy version of the model.