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Hyperspectral unmixing is a very important task for remotely sensed hyperspectral data exploitation. It addresses the (possibly) mixed nature of pixels collected by instruments for Earth observation, which are due to several phenomena including limited spatial resolution, presence of mixing effects at different scales, etc. Spectral unmixing involves the separation of a mixed pixel spectrum into its pure component spectra (called endmembers) and the estimation of the proportion (abundance) of endmember in the pixel. Two models have been widely used in the literature in order to address the mixture problem in hyperspectral data. The linear model assumes that the endmember substances are sitting side-by-side within the field of view of the imaging instrument. On the other hand, the nonlinear mixture model assumes nonlinear interactions between endmember substances. Both techniques can be computationally expensive, in particular, for high-dimensional hyperspectral data sets. In this paper, we develop and compare parallel implementations of linear and nonlinear unmixing techniques for remotely sensed hyperspectral data. For the linear model, we adopt a parallel unsupervised processing chain made up of two steps: i) identification of pure spectral materials or endmembers, and ii) estimation of the abundance of each endmember in each pixel of the scene. For the nonlinear model, we adopt a supervised procedure based on the training of a parallel multi-layer perceptron neural network using intelligently selected training samples also derived in parallel fashion. The compared techniques are experimentally validated using hyperspectral data collected at different altitudes over a so-called Dehesa (semi-arid environment) in Extremadura, Spain, and evaluated in terms of computational performance using high performance computing systems such as commodity Beowulf clusters.