The linkages between term structures separated by finite time periods can be complex. Indeed, in general, the dynamics of the term structure could depend on the entire set of information revealed since the earlier date. This path dependence, which causes difficulties in pricing interest rate claims, is usually eliminated by making specific assumptions on investment behavior or on the evolution of interest rates. In contrast, this article identifies the class of volatility structures that permits the path dependence to be captured by a single sufficient statistic. An equilibrium framework is provided where beliefs and technologies are restricted so that the resulting term structures have volatilities that belong to the restricted class. The models themselves can be characterized by a parsimonious set of parameters and can be initialized to an observed term structure without the introduction of ad-hoc time-varying parameters. Furthermore, since the dynamics of the resulting term structures are two-state Markovian, simple pricing mechanisms can be developed for interest rate claims.