This paper considers a two commodity continuous review inventory system with fixed individual and joint reorder level. The maximum storage capacity for the ith commodity is fixed as S i (i = 1, 2). It is assumed that demand for ith commodity is of unit size and has Poisson distribution with parameter λ i (i = 1, 2). The independent reorder level for ith commodity is fixed as r i and whenever the inventory level of ith commodity falls on r i an order for P i (=S i − r i ) i = 1, 2 items is placed for that commodity irrespective of the inventory level of the other commodity. A joint inventory level s (<min(r 1, r 2)(x + y = s, x = 0, 1,…, s, y = 0, 1,…, s) is fixed for both commodities whenever the inventory level drops to a prefixed level s, an order for and items is placed for both commodities. The limiting probability distribution for the joint inventory levels is computed. Various operational characteristics, expression for the long run total expected cost rate is derived. The results are illustrated with numerical examples.