Standard dynamic models of structural transformation, without knife-edge and counterfactual parameter values, preclude balanced growth path (BGP) analysis. This paper develops a dynamic equilibrium concept for a more general class of models | an alternative to a BGP, which we coin a Stable Transformation Path (STraP). The STraP characterizes the medium-term dynamics of the economy in a turnpike sense; it is the path toward which the economy (quickly) converges from an arbitrary initial capital stock. Calibrated simulations demonstrate that the relaxed parameter values that the STraP allows have important quantitative implications for structural transformation, investment, and growth. Indeed, analyzing the dynamics along the STraP, we show that the modern dynamic model of structural transformation makes progress over the Neoclassical growth model in matching key growth and capital accumulation patterns in cross-country data, including slow convergence.