The model studied by the authors is an integro-differential equation taking the form \(u_t=-u+\lambda(1-u)K*u\) in the space \({\mathbb R}^d,\) where \(\lambda>1\) is a constant, \(K*u\) stands for the convolution, and \(K\geq 0\) is a function such that \(\int_{{\mathbb R}^d} K(z)\, dz=1.\) It is shown that, for certain bounded solutions \(u\) of the afore mentioned equation, the region \(\Omega(t):=\{x\in{\mathbb R}^d:u(x,t)=(\lambda-1)/\lambda\}\) of colonized habitat expands and propagates at large scales with a special speed. The authors call this the phenomenon of front propagation.