Analytical methods have been developed and applied to electron energy loss spectra (EELS) and energy-dispersive X-ray spectra (EDXS) as well as their corresponding two-dimensional elemental maps produced by the computer-controlled analytical electron microscope in BEIB. Deconvolution algorithms developed earlier in the group have been applied to EELS spectra from cryosections of rapidly-frozen chromaffin cells in order to remove effects of plural inelastic scattering and to increase visibility of weak spectral features. In EELS elemental maps counting statistics are not high enough for a complete removal of plural inelastic scattering but sample-thickness effects can be corrected to first order by dividing the core loss signal by the zero-loss signal. Different algoithms for handling X-ray spectra have also been developed and comparison made in terms of accuracy and speed.