Using deep exposures (similar to 10(5) s) with the ROSAT High Resolution Im
ager, we have performed flux-limited surveys for X-ray sources in the vicin
ity of the Hyades-age open stellar clusters NGC 6633 and IC 4756, detecting
31 and 13 sources, respectively. Our primary aim is to search for so-far u
nrecognized cluster members. We propose identifications or classifications
(cluster member, field star, extragalactic field object) for the X-ray sour
ces, based on published membership lists, and on X-ray:optical flux ratios
and optical colour-magnitude diagrams. Results of simulating the expected X
-ray-emitting source populations an compared with the ROSAT measurements an
d with the expected capabilities of the XMM mission. The simulations provid
e a novel method of comparing the activity levels of NGC 6633 and IC 4756 w
ith that of the Hyades. The measurements and simulations confirm that clust
er members are the major class of X-ray emitter in these fields at flux lev
els f(X) greater than or equal to 10(14) erg cm(-2) s(-1) (0 1-2.4 keV), co
ntributing similar to 40 per cent of the total X-ray sources. We find six p
ossible new members in NGC 6633 and four candidates in IC 4756; all require
further observation to establish membership probability.