Hexagonal-close-packed (hcp) γ-precipitates with large aspect ratios form rapidly in some face-centered cubic (fcc) solid-solutions. No model explains the observed time-dependent increase in aspect ratio, nor irregular intermediate growth shapes. We propose a nonequilibrium process involving trapezoidal offshoots (controlled only by energetics) that governs the growth behavior (kinetics) and yields nonequilibrium structures in agreement with observation. Then, combining nucleation theory and diffusion-limited growth both of secondary nuclei and ledges, we derive a general growth equation for γ-precipitates due to solute-segregation to precipitate–matrix interfaces that includes our modification of the Jones–Trivedi model for thickening to account for the slow growth of coherent interfaces compared to incoherent interfaces. The analytic form of nucleation rate agrees in various limits with forms used to fit experimental data, which were not derived from general arguments. In contrast to previous theories, our model yields quantitative agreement to the observed time-dependent increase of aspect ratio, if estimated from the solute supersaturation in the precipitate as well as the dependence on precipitate–matrix interphase energies.