We present a simultaneous Chandra and XMM-Newton observation of the Castor sextett, focusing on Castor A and Castor B, two spectroscopic binaries with early-type primaries. Our study represents the first unambiguous X-ray detection of all three visual components in the Castor sextett making use of the unprecedented spatial resolution of Chandra. Of the present day X-ray instruments only Chandra can isolate the X-ray lightcurves and spectra of Castor A and B (angular separation ~ 4''). We compare the Chandra observation with XMM-Newton data obtained simultaneously. Albeit not able to resolve Castor A and Castor B from each other, the higher sensitivity of XMM-Newton allows for a quantitative analysis of their combined high-resolution spectrum. He-like line triplets are used to examine the temperature and the density in the corona of Castor AB. The oxygen triplet provides a density of ne = (0.5...1) 1010 cm-3, typical for stellar coronae. The analysis for the neon triplet results in much higher densities. By means of a simulated RGS spectrum we estimate the contaminating effect of iron lines to the neon triplet. The temporal variability of Castor AB is studied using data collected with the European Photon Imaging Camera onboard XMM-Newton. Strong flare activity is observed with typical rise times of ~ 10 min and exponential decays which are by a factor of 2-3 slower than the rise. Combining the data acquired simultaneously with Chandra and XMM-Newton each flare can be assigned to its host. Thus we verify that both Castor A and Castor B exhibit flares. Our comparison with the conditions of the coronal plasma of other stars shows that Castor AB behave like typical late-type coronal X-ray emitters supporting the common notion that the late-type secondaries within each spectroscopic binary are the sites of the X-ray production.