We present a systematic study of transport and thermodynamic properties of the Laves phase system Nb 1−y Fe 2+y . Our measurements confirm that Fe-rich samples, as well as those rich in Nb ͑for ͉y͉ Ն 0.02͒, show bulk ferromagnetism at low temperature. For stoichiometric NbFe 2 , on the other hand, magnetization, magnetic susceptibility, and magnetoresistance results point toward spin-density wave ͑SDW͒ order, possibly helical, with a small ordering wave vector Q ϳ 0.05 Å −1 . Our results suggest that on approaching the stoichiometric composition from the iron-rich side, ferromagnetism changes into long-wavelength SDW order. In this scenario, Q changes continuously from 0 to small, finite values at a Lifshitz point in the phase diagram, which is located near y = +0.02. Further reducing the Fe content suppresses the SDW transition temperature, which extrapolates to zero at y Ϸ −0.015. Around this Fe content magnetic fluctuations dominate the temperature dependence of the resistivity and of the heat capacity which deviate from their conventional Fermi-liquid forms, inferring the presence of a quantum critical point. Because the critical point is located between the SDW phase associated with stoichiometric NbFe 2 and the ferromagnetic order which reemerges for very Nb-rich NbFe 2 , the observed temperature dependences could be attributed both to proximity to SDW order or to ferromagnetism.