The regression ofXponX1, · · ·,Xp-1, when the random vectorX= (X1, · · ·,Xp) follows ap-variate (p> 2) Poisson distribution, is obtained. Various sets of sufficient conditions for the linearity of the regression are given. It is shown that the regression is linear in one of the regressors if all the rest are zero, without any restrictions on the distribution ofX.