We calculate the masses of χc(2P ) and χ b (3P ) states with threshold corrections in a coupledchannel model. Here, the meson quarkonium core is augmented by higher Fock components due to pair-creation effects. According to our results, we interpret the resonances characterized by very small threshold corrections, like χ b (3P )'s, as almost pure quarkonia, and those states characterized by non-negligible threshold corrections, like the X(3872), as quarkonium cores plus meson-meson components. We also study the J/ψρ and J/ψω hidden-flavor strong decays of the X(3872). The decays are calculated as the dissociation of one of these components (D 0 D0 * ) into a cc state (J/ψ) plus a light meson (ρ or ω) in a potential model. In particular, our result for the ratio between the X(3872) → J/ψω and J/ψρ widths (0.6) is compatible with the present experimental data (0.8 ± 0.3) within the experimental error.