We present a lattice calculation of the nucleon isovector axial and induced pseudoscalar form factors on the CLS ensembles using Nf = 2 dynamical flavors of nonperturbatively (a)-improved Wilson fermions and an (a)-improved axial current together with the pseudoscalar density. Excited-state effects in the extraction of the form factors are treated using a variety of methods, with a detailed discussion of their respective merits. The chiral and continuum extrapolation of the results is performed both using formulae inspired by Heavy Baryon Chiral Perturbation Theory (HBChPT) and a global approach to the form factors based on a chiral effective field theory (EFT) including axial vector mesons. Our results indicate that careful treatment of excited-state effects is important in order to obtain reliable results for the axial form factors of the nucleon, and that the main remaining error stems from the systematic uncertainties of the chiral extrapolation. As final results, we quote gA = 1.278 ± 0.068- 0.087 +0.000 , (rA2) = 0.360 ± 0.036 -0.088 +0.080 fm 2 , and gP = 7.7 ± 1.8 -2.0 +0.8 for the axial charge, axial charge radius and induced pseudoscalar charge, respectively, where the first error is statistical and the second is systematic.