Fe-57 Mossbauer absorption spectroscopy studies have been performed in zero magnetic field in the temperature range 4.2-200 K, in cobalt ferrite (CoFe2O4) magnetic fluids that differ in the mean size of their particles. For particles with an average diameter of 2 and 3 nm, a quadrupolar doublet progressively replaces the six-line hyperfine field pattern as the temperature increases, This is attributed to a superparamagnetic regime with respect to the time scale tau(M) = 10(-8) s of Fe-57 Mossbauer spectroscopy. For particles with an average diameter of 5 nm, no such superparamagnetic behavior is observed; from the thermal variation of the mean hyperfine field, an axial anisotropy constant K-A = (8 +/- 2) x 10(6) erg cm(-3) is deduced. The whole set of data, together with magnetic measurements, strongly suggests that magnetic anisotropy in these particles has an axial rather than cubic character and that the anisotropy constant varies as the inverse of the square of the particle diameter.