Abstract. -Inelastic neutron scattering has been used to determine the dynamic spin fluctuations in an underdoped high temperature superconductor YBCO 6.8 single crystal. The magnetic resonance, that occurs around 40 meV in overdoped samples, is shifted to a lower energy, E r = 34 meV. A constant ratio, E r /k B T C = 4.9 ± 0.2, almost independent of the doping level, is found. According to numerous theoretical approaches, this finding supports the idea that the resonance energy is proportional (approximately twice) to the superconducting gap. The electronic correlations in high-T C superconductors are crucial in understanding normal as well as superconducting (SC) properties. They have been experimentally evidenced by the persistence of spin fluctuations in the metallic state of cuprates. Especially, inelastic neutron scattering (INS) experiments have allowed to investigate the wavevector, energy and the doping dependencies of the imaginary part of the generalized magnetic susceptibility (Imχ) on a unique sample of YBa 2 Cu 3 O 6+x (YBCO) in its metallic state [1,2,3]. First, Imχ is still located at the antiferromagnetic (AF) wavevector, Q AF = (1/2, 1/2, q l ) ≡ (π, π). Second, in the SC state, when going from the weakly-doped regime x ≃ 0.5 to fully oxidized sample x ≃ 1[3], Imχ is gradually restricted to a smaller energy range. It is shifted to higher energies with increasing x by a doping dependant energy gap [1,2,3,4], called spin-gap. In optimally doped samples and overdoped samples (x ≥ 0.94), it is now well established that a strong sharp magnetic peak appears around 40 meV, called resonance by J. Rossat-Mignod et al [1] for its first evidence. Its magnetic origin has been then confirmed by using polarized neutron scattering [5]. Its major characteristic is that it disappears above T C [1,3,4,6]. This peak also occurs in Imχ in addition to another contribution which stands in the normal state [1,3]. However, this part of Imχ is so reduced with increased doping [3,4] that it becomes hardly detectable [4,6,7] in fully oxydized samples.The origin of this magnetic resonance has been extensively discussed, especially in itinerant magnetism descriptions [8,9,10,11,12,13,14]. Beyond all the different hypotheses in these approaches, one can basically consider that an enhancement of the electronic spin susceptibility arises at a specific energy due to the opening of the SC gap. This is usually argued to support a d x 2 −y 2 symmetry for the SC order parameter, ∆ k [8,9,10,11,12,13,15] , iii) because of a collective mode in the particle-particle channel in the Hubbard model [10]. Other approaches propose that this resonance results from spin-flip charge carriers excitations across the SC gap [11,12,13,14,15]. In this view, the resonance energy, E r , closely reflects the amplitude of the SC gap as well as its doping dependence. However, the behaviour of the resonance peak in the underdoped regime remains unclear. So far, only short reports of a previous investigation at x ≃ 0.83 [2,3] have emphasized that crucial...