Functional Magnetic Resonance Imaging (fMRI) and Electropencephalography (EEG) are the two techniques that are most often used to study the working brain. With the first technique we use the MRI machine to measure where in the brain the supply of oxygenated blood increases as result of an increased neural activity with a high precision. The temporal resolution of this measure however is limited to a few seconds. With EEG we measure the electrical activity of the brain with millisecond precision by placing electrodes on the skin of the head. We can think of the EEG signal as a signal that consists of multiple superimposed frequencies that vary their strength over time and when performing a cognitive task. Since we measure EEG at the level of the scalp, it is difficult to know where in the brain the signals exactly originate from. For about a decade we are able to measure fMRI and EEG at the same time, which possibly enables us to combine the superior spatial resolution of fMRI with the superior temporal resolution of EEG. To make this possible, we need to understand how the EEG signal is related to the fMRI signal, which is the central theme of this thesis. The main finding in this thesis is that increases in the strength of EEG frequencies below 30 Hz are related to a decrease in the fMRI signal strength, while increases in the strength of frequencies above 40 Hz is related to an increase in the strength of the fMRI signal. Changes in the strength of the low EEG frequencies are however are not coupled to changes in high frequencies. Changes in the strength of low and high EEG frequencies therefore contribute independently to changes in the fMRI signal.