We let $\rho(r)$ be a fixed infinitely differentiable function of $r=(x^2_1+\dots+x_m^2)^{1/2}$ satisfying the properties (i) $\rho\geq0$, (ii) $\rho(r)=0$, $r\geq1$, (iii) $\rho(r)dx=1$. The function $\delta_n(x)$, with $x$ in $R^m$, is then defined by $\delta_n(x)=n^m\rho(nr)$ for $n=1,2,\dots$. The product $f\circ g$ of two distributions $f$ and $g$ is then defined to be the neutrix limit of the sequence $\{fg_n\}$, where $g_n=g*\delta n$. Some results are given.