In the zero temperature limit, the zero-point quantum fluctuations of certain degrees of freedom (or quantum criticality) is claimed to describe the collective fluctuations of systems undergoing a second-order phase-transition. To date, some of the best studied examples of quantum phasetransitions, and concomitant anomalous physical behavior, involve f −electron magnetism in heavyfermion metals, where quantum criticality (QC) is ascribed to either the suppression of a spindensity wave (SDW) ground-state or the Kondo-effect. Here, we unveil evidence for a quantum phase-transition in CeCu2Ge2 which displays both an incommensurate spin-density wave (SDW) ground-state, and a strong renormalization of the quasiparticle effective masses (µ) due to the Kondo-effect. For all angles θ between an external magnetic field (H) and the crystallographic c−axis, the application of H leads to the suppression of the SDW-state through a 2 nd -order phasetransition at a θ−dependent critical-field Hp(θ) leading to the observation of small Fermi surfaces (FSs) in the paramagnetic (PM) state. For H c-axis, these FSs are characterized by light µs pointing also to the suppression of the Kondo-effect at Hp with surprisingly, no experimental evidence for quantum-criticality (QC). But as H is rotated towards the a-axis, these µs increase considerably becoming undetectable for θ > 56• between H and the c-axis. Around H a p ∼ 30 T the resistivity becomes ∝ T which, coupled to the divergence of µ, indicates the existence of a field-induced QC-point at H a p (T = 0 K). This observation, suggesting FS hot-spots associated with the SDW nesting-vector, is at odds with current QC scenarios for which the continuous suppression of all relevant energy scales at Hp(θ, T ) should lead to a line of quantum-critical points in the H − θ plane. Finally, we show that the complexity of its magnetic phase-diagram(s) makes CeCu2Ge2 an ideal system to explore field-induced quantum tricritical and QC end-points.