Magnetic Resonance Imaging (MRI) and magnetic resonance spectroscopic imaging (MRSI) play an important role in the noninvasive diagnosis of brain tumours. We investigate the use of both MRI and MRSI, separately and in combination with each other for classification of brain tissue types. Many clinically relevant classification problems are considered; for example healthy versus tumour tissues, low- versus high-grade tumours. Linear as well as nonlinear techniques are compared. The classification performance is evaluated by the area under the receiver operating characteristic (ROC) curve (AUC). In general, all techniques achieve a high performance, except when using MRI alone. For example, for low- versus high-grade tumours, low- versus high-grade gliomas, gliomas versus meningiomas, respectively a test AUC higher than 0.91, 0.93 and 0.98 is reached, when both MRI and MRSI data are used.