“…In the sequel, simultaneous controllability engaged many authors like S. A. Avdonin and W. Moran in [6], M. Tucsnak and G. Weiss [7], who proved the simultaneous exact controllability of two systems, F. Ammar Khodja et al([8]) who worked on the null controllability of two parabolic semilinear equations, and M. González-Burgos and L. de Teresa who addressed the problem for a system of m (m 1) parabolic linear coupled equations (see [9]). Recently, the author examined in [10] the simultaneous null controllability with constrained control for a parabolic system of two linear coupled equations, and the present work extends the latter results. …”