We have conducted a detailed study of the object NGC 2451, which actually consists of two different open clusters A and B along the same line of sight at 206 pc and 370 pc distance, respectively. Although belonging to the nearest clusters, they have not been much investigated until present due to strong contamination by field stars. ROSAT X-ray observations and optical UBVR photometry are used to identify cluster members by means of X-ray emission and colour-magnitude diagrams. The identified stars concentrate nicely around the expected main sequences in the colour-magnitude diagram at the distances derived from astrometric investigations. Altogether, 39 stars are identified as member candidates of the nearer cluster A, 49 stars as member candidates of the more distant cluster B, and 22 faint stars are probably members of either of the two clusters, but due to large errors it is not clear to which one they belong. Further 40 stars identified with X-ray sources are probably non-members. For the first time, the range of known probable cluster members of NGC 2451 A and B has been extended downwards the main sequence to stars of spectral class M. Isochrone fitting yields an age of 50 to 80 Myrs for NGC 2451 A and ~50 Myrs for NGC 2451 B, consistent with the X-ray luminosity distribution functions, which are comparable to other clusters in the same age range. Except from the occurence of four flares, the stars of both clusters do not show strong long-term X-ray variability exceeding a factor 5 over a time span of 1 to 3 years. Based on observations performed by the ROSAT X-ray observatory and the European Southern Observatory. Tables 3-6 are only available in electronic form at http://www.edpsciences.org