Properties of high redshift clusters are a fundamental source of information for cosmology .
It has been shown by Oukbir and Blanchard ( 1997 ) that the combined knowledge of the redshift distribution of X-ray clusters of galaxies and the luminosity-temperature correlation , L _ { X } - T _ { X } , provides a powerful test of the mean density of the Universe .
In this paper , we address the question of the possible evolution of this relation from an observational point of view and its cosmological significance .
We introduce a new indicator in order to measure the evolution of the X-ray luminosity-temperature relation with redshift and take advantage of the recent availability of temperature information for a significant number of high and intermediate redshift X-ray clusters of galaxies .
From our analysis , we find a slightly positive evolution in the L _ { X } - T _ { X } relation .
This implies a high value of the density parameter of 0.85 \pm 0.2 .
However , because the selection of clusters included in our sample is unknown , this can be considered only as a tentative result .
A well-controlled X-ray selected survey would provide a more robust answer .
XMM will be ideal for such a program .