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We investigate the cosmology of x-matter with pressure, p[sub x], and density, ρ[sub x], related by p[sub x]=w[sub 0]ρ[sup γ][sub x](w[sub 0]<0;γ >0). For γ >1, this x-matter behaves like a cosmological constant when a≪ a[sub 0] (a being the scalefactor and a[sub 0] the scalefactor at present) and like matter for a γ a[sub 0]; for γ <1, the behaviour is the opposite; for γ =1, the x-matter density varies as a[sub -3](1+w[sub 0]). Models of x-matter with γ >1 reach, at all times, densities lower than do models with γ ≤ 1 for equal present x-matter density, so the former have less effect on the formation of structures in the Universe. Allowed values for the free parameters of these cosmological models are estimated by imposing two observational constraints which originate from the age problem of the Universe and from the luminosity--distance relation for Type Ia supernovae at z=0.4. [ABSTRACT FROM AUTHOR]