Some problems of the quantitative analysis of diffusible elements in cryosections are reviewed. The two prevalent methods for obtaining concentrations from X-ray data, one based on characteristic radiation alone and the other on continuum-normalization, are recapitulated. Both methods seem suitable at cellular level while the latter seems preferable at finer spatial resolution. Recourse to both methods together is desirable in the analysis of frozen-hydrated sections especially when there is no peripheral standard. Selective local contamination is a particular hazard in the analysis of chlorine. In the case of sodium, physical parameters set restrictive limits to the minimum concentration measurable by 'energy-dispersive' X-ray spectrometry (about 20 mM kg-1) and to the spatial resolution attainable by diffractive X-ray spectrometry (approximately 0.2 micrometer). One obvious danger to meaningful quantitative analysis is inadvertent redistribution of diffusible elements during the moments preceding the freeze-quenching of a tiny piece of tissue. Data are presented to show that concentration changes due to simple evaporation are a real hazard prior to the quenching of sub-millimetre size samples.