We present a reinvestigation of the complex magnetic phase diagram of
the heavy-fermion system Ce(Cu1-xNix)(2)Ge-2 by employing measurements
of the specific heat, C(T), and thermal expansion, alpha(T), on high-
quality single crystals with x = 0, 0.02, 0.05, 0.5 and 0.8 in magneti
c fields B less than or equal to 8T. In addition to what was observed
in polycrystalline samples multiple phase-transition anomalies could b
e resolved in these single crystals for x<0.5 and 1.5 K < T < T-N Shar
p anomalies in C(T) and thermal hysteresis in a(T) give evidence that
these transitions are of first order (x = 0.02, 0.05). Our findings de
monstrate that the structure of the antiferromagnetically ordered stat
e depends on subtle changes of the hybridization of the Ce-4f state to
its local environment, while the interplay of Kondo- and RKKY-interac
tion, which determines the existence of a long-range ordered state is
governed by volume and/or density-of-states effects.