The paper under review studies the semigroup \(W(t)\) generated by a general neutron transport equation \[ {{\partial f}\over {\partial t}} + v \cdot{{\partial f}\over {\partial x}} + \sigma (x,v) f(x,v,t) -\int_V k(x,v,v') f(x,v',t)\,d\mu(v')=0 \] in \(L^p(\Omega\times V)\), subject to a suitable boundary condition. Here \(\Omega\) is a smooth open subset of \({\mathbb R}^n\), \(\mu\) is a Radon measure on \({\mathbb R}^n\) with support~\(V\), \(\sigma \in L^\infty(\Omega\times V)\) is the collision frequency, and \(k\) is the scattering kernel. If \(k=0\), then the above equation generates the streaming semigroup \(U(t)\) in~\(L^p(\Omega\times V)\). The author gives sufficient conditions for the measure \(\mu\) and the integral scattering operator \(K\) corresponding to the kernel \(k\) in order that \(W(t)-U(t)\) be compact on \(L^p(\Omega\times V)\) and shows that these conditions are in a sense optimal.