Summary: We study the possibility of simultaneous blow-up for positive solutions of a system of two heat equations, \(u_t=\Delta u\), \(v_t=\Delta v\), in a bounded smooth domain \(\Omega\), with boundary conditions \({\partial u\over\partial\eta}= u^{p_{11}} v^{p_{12}}\), \({\partial v\over\partial\eta}= u^{p_{21}} v^{p_{22}}\). We prove that if \(u\) blows up then \(v\) can fail to blow-up if and only if \(p_{11}> 1\) and \(p_{21}> p_{11}- 1\).