Few-body models are often used in nuclear physics to describe the scattering of composite systems, such as halo nuclei. The adiabatic approximation provides a simplification of the few-body Schrodinger equation so that breakup of the projectile may be included in a closed form. It assumes that the breakup channels are degenerate with the ground state, allowing all the bound and continuum breakup states to be mapped onto a single channel. In this thesis, the first order corrections to the adiabatic approximation are presented, at energies in the range of 5-50 MeV per nucleon. The systems studied are the elastic scattering of 11Be and 6He from a 12C target. The non-adiabatic corrections were calculated within two models: (i) The core recoil model - When the scattering is dominated by the core-target interaction, neglecting the valence-target interaction provides an analytical solution of the adiabatic wavefunction. Corrections to the adiabatic approximation can only arise in this model through recoil of the core. The corrections were calculated both in the eikonal approximation and exactly. (ii) The Glauber model - The semi-classical eikonal approximation is made in addition to the adiabatic approximation, to include the core and valence-target interactions. Non-adiabatic corrections in this model include contributions from both core and valence recoil. The non-adiabatic corrections were found to be smaller than expected from qualitative arguments. This was shown to be due to the large absorption associated with the scattering of the core by the target. In the core recoil model, for core potentials with large imaginary components, the eikonal approximation was found to give a good description of the corrections, while for weak imaginary potentials it did not account for the large angle behaviour of the corrections correctly. In the Glauber model, the non-adiabatic corrections were dominated by the valence recoil term which was not accurately described in the Glauber model, due to its weak imaginary potential and the use of the eikonal approximation to calculate the corrections.