This paper proposes a constructive design of boundary controllers for globally (practically) Kappa(infinity)-exponential stabilization of extensible and unshearable marine risers with large in-plane deflection under sea loads. Linearization or Maclaurin expansion of the strain and cross section rotation are not required. The control design is based on the Lyapunov direct method. Well-posedness and stability of the closed-loop system are analyzed by two Lyapunov-type theorems developed for study of existence and uniqueness, and stability of nonlinear evolution systems in Hilbert space. (C) 2016 Elsevier Ltd. All rights reserved.