In SU(2) lattice gauge theory, we study deviations from ideal gas behaviour near the deconfinement point. On lattices of sizeN [sigma] 3 ×4,N [sigma]=8, 12, 18 and 26, we calculate the quantity [Delta]= [epsilon]–3P)/T 4. It increases sharply just above T c , peaks at T/T c =1.15 ±0.05 and then drops quickly. This form of behaviour is shown to be the consequence of a second order phase transition. Dynamically it could arise because just above T c , the low momentum states of the system are remnant massive modes rather than deconfined massless gluons.