Dynamical Systems (DS) for robot motion modeling are a promising approach for efficient robot learning and control. Our focus in this paper is on autonomous dynamical systems, which represent a motion plan without dependency on time. We develop a method that allows to locally reshape an existing, stable nonlinear autonomous DS while preserving important stability properties of the original system. Our system is based on local transformations of the dynamics. We propose an incremental learning algorithm based on Gaussian Processes for learning to reshape dynamical systems using this representation. The approach is validated in a 2d task of learning handwriting motions, a periodic polishing motion and in a manipulation task with the 7 degrees of freedom Barrett WAM manipulator. (C) 2015 Elsevier B.V. All rights reserved.