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The results of an intercalibration between the extreme ultraviolet spectrometers Coronal Diagnostic Spectrometer (CDS) and Solar Ultraviolet Measurements of Emitted Radiation (SUMER) onboard the Solar and Heliospheric Observatory (SOHO) are presented. During the joint observing program Intercal_01, CDS and SUMER were pointed at the same locations in quiet Sun areas and observed in the same wavelength bands located around the spectral lines He i 584 A, Mg x 609 A, and Mg x 624 A. The data sets analyzed here consist of raster images recorded by the CDS normal-incidence spectrometer and SUMER detector A and span the time from March 1996 to August 1996. Effects of the different spatial and spectral resolutions of both instruments have been investigated and taken into account in the analysis. We find that CDS measures generally a 30% higher intensity than SUMER in the He i 584-A line, while it measures 9% and 17% higher intensities in Mg x 609 A and Mg x 624 A, respectively. Both instruments show very good temporal correlation and stability, indicating that solar variations dominate over changes in instrumental sensitivity. Our analysis also provides in-flight estimates of the CDS spatial point-spread functions.