The wave front $WF(G_k)$ of an arbitrary Feynman diagram with $k$ external vertices is described. It is shown that $G_2(x_1,x_2)$ can have singularities only for $(x_1-x_2)^2=0$ , and $G_3(x_1,x_2,x_3)$ only when $(x_j-x_{j'})^2=0$ for certain $j\ne j'$ . It is shown that in the case of four or more external vertices the simplest diagrams have singularities not only on the light cones with respect to $x_j-x_{j'}$ .