A new contourlet domain image watermark detector is proposed in the present study. As the performance of the detector completely depends on the accuracy of the statistical model, the contourlet coefficients and statistical properties are studied first. The heavy-tailed distribution and heteroscedasticity of these coefficients are demonstrated in this study. These characteristics cannot be captured simultaneously by the models, which are proposed previously. A two-dimensional generalised autoregressive conditional heteroscedasticity (2D GARCH) model is suggested to overcome this problem. Dependencies of the contourlet coefficients can be explained by the efficient structure provided by this model. A 2D GARCH model-based contourlet domain watermark detector is designed and its performance analysed by computing the receiver operating characteristics. The high accuracy of the proposed detector, its robustness under several types of attacks, and its outperformance compared to alternative watermarking methods are verified by the obtained experimental results.