A detailed elastic neutron scattering study of the structural and magnetic phase transitions in single-crystal SrFe2As2 reveals that the orthorhombic (O)-tetragonal (T) and the antiferromagnetic transitions coincide at TO=TN=(201.5±0.25) K. The observation of coexisting O-T phases over a finite temperature range at the transition and the sudden onset of the O distortion provide strong evidences that the structural transition is first order. The simultaneous appearance and disappearance within 0.5 K upon cooling and within 0.25 K upon warming, respectively, indicate that the magnetic and structural transitions are intimately coupled. We find that the hysteresis in the transition temperature extends over a 1–2 K range. Based on the observation of a remnant orthorhombic phase at temperatures higher than TO, we suggest that the T-O transition may be an order-disorder transition.