We have studied the magnetic dynamics in nanocrystalline samples of α-Fe2O3 (hematite) and NiO by inelastic neutron scattering. By measuring around the structural and the antiferromagnetic reflections, we have probed uniform and staggered magnetic oscillations, respectively. In the hematite particles, we observed a clear double peak in the energy distribution of the antiferromagnetic signal, in addition to a quasi-elastic peak. We interpret the double peak to represent collective magnetic excitations. Broadening of the central quasi-elastic peak with increasing temperature is interpreted as a sign of superparamagnetic relaxation. Studies of the antiferromagnetic signal from NiO also show evidence of collective magnetic excitations, but with a higher energy of the precession states than for hematite. The inelastic signal at the structural reflection of NiO presents evidence for uniform magnetic oscillations very similar to the antiferromagnetic signal, as is expected for a simple antiferromagnet. The hematite sample did not show any signs of uniform oscillations, although these have been predicted theoretically.