- In order to produce specific complex structures from a large set of similar biochemical building blocks, many biochemical systems require high sensitivity to small molecular differences. The first and most common model used to explain this high specificity is kinetic proofreading, which has been extended to a variety of systems from detection of DNA mismatch to cell signaling processes. While the specification properties of kinetic proofreading models are well known and were studied in various contexts, very little is known about their temporal behavior. In this work, we study the dynamical properties of discrete stochastic two-branch kinetic proofreading schemes. Using the Laplace transform of the corresponding chemical master equation, we obtain an analytical solution for the completion time distribution. In particular we provide expressions for the specificity as well as the mean and variance of the process completion times. We also show that, for a wide range of parameters, a process distinguishing between two different products can be reduced to a much simpler three-point process. Our results allow for the systematic study of the interplay between specificity and completion times, as well as testing the validity of the kinetic proofreading model in biological systems.