We consider, in a completely model-independent way, the transfer of energy between the components of the dark energy sector consisting of the cosmological constant (CC) and that of relic neutrinos. We show that such a cosmological setup may promote neutrinos to mass-varying particles, thus resembling a recently proposed scenario of Fardon, Nelson, and Weiner (FNW), but now without introducing any acceleronlike scalar fields. Although a formal similarity of the FNW scenario with the variable CC one can be easily established, one nevertheless finds different laws for neutrino mass variation in each scenario. We show that as long as the neutrino number density dilutes canonically, only a very slow variation of the neutrino mass is possible. For neutrino masses to vary significantly (as in the FNW scenario), a considerable deviation from the canonical dilution of the neutrino number density is also needed. We note that the present 'coincidence' between the dark energy density and the neutrino energy density can be obtained in our scenario even for static neutrino masses. * horvat@lei3.irb.hr 1 It is today firmly established experimentally that neutrinos have nonzero masses and nontrivial mixings, thus pointing to the existence of physics beyond the standard model.In addition, relic neutrinos in the universe, being the second most abundant particles in the universe, also play an important role in measuring neutrino mass with cosmological data, in setting bounds on nonstandard neutrino properties, and also in solving some of the cosmological problems.Another great discovery in recent years has been an observation of the accelerating rate of expansion of the universe, usually attributed to some mysterious dark energy sector. The that although the number density of neutrinos dilutes canonically (∼ a −3 ), the masses of neutrinos change almost inversely (∼ a −3ω ), thereby promoting their energy density to an almost undilutable substance. Hence relic neutrinos become tightly coupled to the original dark energy fluid. If this can be kept for most of the history of the universe, the near coincidence at present, ρ Λ ∼ ρ ν , will cease to be perceptive as a coincidence at all.For models with variable mass neutrinos prior to the proposal [2] see [6], and for those who discussed neutrino mass in connection with dark energy, see [7]. Application of the FNW proposal includes some studies on leptogenesis [8], solar neutrinos [9], and also on the cosmo MSW effect [10].In the present paper we show how the variable but "true" cosmological constant (CC), with the equation of state (EOS) ω Λ ≡ p Λ /ρ Λ being precisely -1, may give rise to scale-2 dependent neutrino masses, in the absence of any acceleronlike scalar fields. Throughout the paper we always highlight those points in which our scenario differs from the FNW one. Models with the variable CC which could successfully mimic quintessence models and may also shed some light on the coincidence problem (between dark energy and dark matter), have been put forward recently. E...