GOCE will be the first satellite ever to measure the second order derivatives of the Earth's gravitational potential in space. With these measurements it is possible to derive a high accuracy and resolution gravitational field if systematic errors and/or outliers have been removed to the extent possible from the data. It is necessary to detect as many outliers as possible in the data pre-processing because undetected outliers may lead to erroneous results when the data are further processed, for example in the recovery of a gravity field model. Outliers in the GOCE gravity gradients, as they are likely to occur in the real observations, will be searched for and detected in the processing step preceding gravity field analysis. As the diagonal gravity gradients are the main gradient observables for GOCE, three methods are discussed to detect outliers in these gradients. The first is the tracelessness condition, that is, the sum of the diagonal gradients has to be zero. The second method compares GOCE gravity gradients with model or filtered gradients. Finally, along track interpolation of gravity gradient anomalies is discussed. Since the difference between an interpolated value and a measured value is large when outliers are present, along track interpolation is known to be suitable for outlier detection. The advantages and disadvantages of each method are discussed and it is shown that the final outlier detection algorithm, which is a combination of the three methods, is able to detect almost all outliers while the number of falsly detected outliers remains small.