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P>Intensive global positioning system (GPS) monitoring after the 1999 Izmit earthquake provides an opportunity to understand the postseismic behaviour of a strike-slip fault and the rheology below the brittle upper crust. Two data sets are available: displacements measured during the first 300 days after the Izmit earthquake and velocity measurements between 2003 and 2005. Using an inversion method and a forward modelling, respectively, we investigate two mechanisms: (1) afterslip on and below the coseismic rupture plane and (2) viscoelastic stress relaxation in the lower crust and upper mantle described by a Maxwell or a standard linear solid (SLS) rheology. The inversion results show that the first several months following the Izmit earthquake were dominated by afterslip at depths shallower than 30 km and the slip amount decayed with time; after that, apparent afterslip has a very different spatial distribution and is located much deeper. For viscoelastic relaxation, a model with an elastic upper crust and a Maxwell viscoelastic lower crust overlying a Maxwell mantle (E-M-M) fits the data measured in the first 300 days better in the far field than in the near field. However, the observed far-field, 300-day displacement and the long-term (2003-2005) displacement, which might be dominated by viscoelastic relaxation, cannot be described by a Maxwell rheological model with constant viscosity: the effective viscosity increases over time. Therefore, we have built a refined rheological model: an elastic upper crust and an SLS lower crust overlying a Maxwell viscoelastic mantle (E-SLS-M). Our best solution yields a viscosity for the lower crust of similar to 2 x 10(18) Pa s, a relaxation strength of 2/3 and a viscosity for the Maxwell mantle of 7 x 10(19) Pa s. Finally, we explain the data using a composite model, consisting of the preferred E-SLS-M model and the afterslip model obtained from the residual displacement after correcting for viscoelastic relaxation. For the early time period, the residual displacements can be mainly explained by a shallow afterslip whose magnitude decays with time and whose spatial distribution is stable, whereas the residual displacements for the later time period require negligible afterslip. It indicates that the postseismic deformation in the later time period induced by a deep source can be almost entirely explained by the E-SLS-M model. The composite model can generally explain the data in the entire spatial and temporal space.