The [Ru(bpy)3][LiCr(ox)3] system (bpy = 2,2'-bipyridine, ox = oxalate) has two crystallographically non-equivalent [Cr(ox)3]3- sites. In steady-state resonant and nonresonant fluorescence line narrowing (FLN) experiments on the R1 lines of the two non-equivalent [Cr(ox)3]3- chromophores, multiline spectra are observed at 1.6 K. Such multiline spectra are clear evidence for resonant energy transfer processes within the inhomogeneously broadened R1 lines. In addition, time-resolved experiments show that also site-to-site energy transfer occurs, which turns out to be resonant, too, however with a non-negligible phonon-assisted contribution even at 1.5 K.