  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 $\mid y\mid\geq 0.02$), show
bulk ferromagnetism at low temperature. For stoichiometric NbFe$_2$, on the
other hand, magnetization, magnetic susceptibility and magnetoresistance
results point towards spin-density wave (SDW) order, possibly helical, with a
small ordering wavevector $Q \sim 0.05$ \AA$^{-1}$. 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
$y\approx -0.015$. 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.
