Inelastic neutron scattering measurements have been carried out on the heavy fermion superconductor UNi2Al3. This hexagonal material orders magnetically into an incommensurate structure, characterized by the ordering wave vector Qord= (1/2± τ, 0, 1/2) with τ∼0.11, below TN=4.6 K and then superconducts below TC = 1.2 K. For energies above 2 meV, we observe quasielastic magnetic neutron scattering both near (0, 0, n/2) and in ridges along H of the form (H, 0, n/2), with n odd. This scattering has a characteristic energy width of ∼6 meV, and evolves on a temperature scale of ∼80 K, which is close to the coherence temperature of this heavy fermion metal. High energy resolution measurements, below 2 meV, show the spectral weight of these fluctuations to evolve from the commensurate wavevector (0, 0, n/2), with n odd, to the material's incommensurate ordering wave vector as the energy of the fluctuations decreases. This observation is particularly interesting in light of the fact that UNi2Al3's isostructural sister heavy fermion superconductor, UPd2Al3, orders into a commensurate antiferromagnetic structure with this same (0, 0, n/2) wave vector. A search for inelastic magnetic scattering associated with the superconducting phase transition, as has been observed in UPd2Al3, revealed no additional scattering at the incommensurate ordering wavevector and energies above 0.10 meV. Measurements of the low-lying acoustic phonons were also performed, and show zone boundary energies lying in the range 10-13 meV.