A two commodity continuous review inventory system with independent Poisson processes for the demands is considered in this paper. The maximum inventory level for the i-th commodity fixed as $S_i$(i = 1,2). The net inventory level at time t for the i-th commodity is denoted by $I_i(t),;i;=;1,2$. If the total net inventory level $I(t);=;I_1(t)+I_2(t)$ drops to a prefixed level s $[{leq};frac{({S_1}-2}{2};or;frac{({S_2}-2}{2}]$, an order will be placed for $(S_{i}-s)$ units of i-th commodity(i=1,2). The probability distribution for inventory level and mean reorders and shortage rates in the steady state are computed. Numerical illustrations of the results are also provided.