We report specific heat measurement in a broad temperature range between 0.
06 and 20 K on single crystalline CeRu2Si2 in magnetic fields applied paral
lel to the c-direction around the critical field B-M , where the meta-magne
tic transition from the itinerant to the localized state takes place. In th
e critical field B-M \\ c = 7.8 T a distinct deviation fro the usual Fermi-
liquid behaviour is found down to our lowest temperature. Below 1.8 K C/T v
aries as (1-aT), while for 1.8 K < T < 20 K a power law Tlambda-1 with lamb
da = 0.66 is found. Small deviation from the critical magnetic field leads
to the recovery of a Fermi-liquid ground state. The observed behavior of th
e specific heat at the field induced magnetic instability is discussed in t
he context of a non-Fermi-liquid state and compared with those for the fiel
d-induced nFl CeCu6-x Ag-x and the recent observation of nFl behavior at B-
M in UPt3.