Images with high spatial and spectral resolutions are desirable for remote sensing applications. Unfortunately, due to sensor physical constraints, this result cannot be obtained by a single sensor. To overcome these limitations, a great number of data fusion approaches have been developed in the last years. The fusion of panchromatic and multispectral images, also known as Pansharpening, is capturing a lot of attention in the literature. In this paper, we extend and analyze the use of some classical pansharpening techniques, belonging to the MultiResolution Analysis and Component Substitution families, for fusing hyperspectral data instead of multispectral ones. The experimental results, conducted on two real datasets acquired by the Hyperion/ALI and CHRIS-Proba/QuickBird sensors, point out the greater suitability of the algorithms into the MRA class thanks to a better spectral consistency of the final products, which is a desirable feature when the number of bands to fuse increases.