We consider linear and nonlinear convergence acceleration techniques in the framework of Newton or inexact Newton methods. The proposed procedure is based on a new dynamic preconditioner to be used in combination with the GMRES method for reducing the cost of solving a sequence of linear systems. A nonlinear convergence acceleration technique based on a previous work by Washio et al. is also added. The benefits of this combination of acceleration techniques is shown on fluid-structure interaction problems in haemodynamics for two- and three-dimensional applications.