  We analyzed the luminosity-temperature (L-T) relation for 2 samples of galaxy
clusters which have all been observed by the ASCA satellite. We used 32 high
redshift clusters (0.3<z<0.6), 53 low redshift clusters (z<0.3), and also the
combination of the low and high redshift datasets. We assumed a power law
relation between the bolometric luminosity of the galaxy cluster and its
integrated temperature and redshift (L_{bol,44}=C*T^alpha*(1+z)^A). The results
are consistent, independent of cosmology, with previous estimates of
L$\sim$T$^3$ found by other authors. We observed weak or zero evolution.
