This paper focuses on dynamic output feedback control of a broad class of nonlinear two-timescale processes modeled within the mathematical framework of singular perturbations. A sequential procedure is employed to synthesize a nonlinear well-conditioned two-time-scale output feedback controller, which guarantees stability and enforces output tracking in the closed-loop system, provided that the separation of the slow and fast dynamics of the two-time-scale process is sufficiently large. The proposed controller is successfully applied to two-time-scale chemical processes, a series of two chemical reactors and a fluidized catalytic cracker, and is shown to outperform output feedback controller design methods that do not account for the presence of time-scale multiplicity.