The critical behaviour of a semi-infiniten-vector model with a surface term (c/2) ∫dSφ2 is studied in 4-e dimensions near the special transition. It is shown that all critical surface exponents derive from bulk exponents and η∥, the anomalous dimension of the order parameter at the surface. The surface exponents and the crossover exponent Φ for the variablec are calculated to second order in e. It is found that Φ does not satisfy the relation Φ=1-ν predicted by Bray and Moore. The order-parameter profilem(z)= is calculated to first order in e. In contrast to mean-field theory,m(z) is not flat nor does it satisfy a Neumann boundary condition. General aspects of the field-theoretic renormalization program for systems with surfaces are discussed with particular attention paid to the explanation of the unfamiliar new features caused by the presence of surfaces.