Alzheimer's Diasese (AD) diagnosis can be carried out by analysing functional or structural changes in the brain. Functional changes associated to neurological disorders can be figured out by positron emission tomography (PET) as it allows to study the activation of certain areas of the brain during specific task development. On the other hand, neurological disorders can also be discovered by analysing structural changes in the brain which are usually assessed by Magnetic Resonance Imaging (MRI). In fact, computer-aided diagnosis tools (CAD) that have been recently devised for the diagnosis of neurological disorders use functional or structural data. However, functional and structural data can be fused out in order to improve the accuracy and to diminish the false positive rate in CAD tools. In this paper we present a method for the diagnosis of AD which fuses multimodal image (PET and MRI) data by combining Sparse Representation Classifiers (SRC). The method presented in this work shows accuracy values up to 95% and clearly outperforms the classification outcomes obtained using single-modality images.