In operations research, the equipment replacement process is usually modeled in discrete time. An alternative approach is represented by continuous-time vintage capital models that explicitly involve the equipment lifetime and are described by nonlinear integral equations. The paper introduces and analyzes a model that unites both these approaches. The structure of optimal replacement, transition, and long-term dynamics, and clustering and splitting of replaced machines are discussed and illustrated with numeric examples. Equipment splitting is demonstrated when the optimal equipment lifetime increases. © 2010 International Federation of Operational Research Societies.