Hyperspectral imagery is a new class of image data which is mainly used in remote sensing. It is characterized by a wealth of spatial and spectral information that can be used to improve detection and estimation accuracy in chemical and biological standoff detection applications. Finding spectral endmembers is a very important task in hyperspectral data exploitation. Over the last decade, several algorithms have been proposed to find spectral endmembers in hyperspectral data. Existing algorithms may be categorized into two different classes: 1) endmember extraction algorithms (EEAs), designed to find pure (or purest available) pixels, and 2) endmember generation algorithms (EGAs), designed to find pure spectral signatures. Such a distinction between an EEA and an EGA has never been made before in the literature. In this paper, we explore the concept of endmember generation as opposed to that of endmember extraction by describing our experience with two EGAs: the optical real-time adaptative spectral identification system (ORASIS), which generates endmembers based on spectral criteria, and the automated morphological endmember extraction (AMEE), which generates endmembers based on spatial/spectral criteria. The performance of these two algoriths is compared to that achieved by two standard algorithms which can perform both as EEAs and EGAs, i.e., the pixel purity index (PPI) and the iterative error analysis (IEA). Both the PPI and IEA may also be used to generate new signatures from existing pixel vectors in the input data, as opposed to the ORASIS method, which generates new spectra using an minimum volume transform. A standard algorithm which behaves as an EEA, i.e., the N-FINDR, is also used in the comparison for demonstration purposes. Experimental results provide several intriguing findings that may help hyperspectral data analysts in selection of algorithms for specific applications.