This study developed deterministic inventory models for deteriorating items in a declining market when a delay in payments is permissible. The cycle times of inventory policies are constant and the credit period is also a known constant. The items are deteriorating at a constant rate and the demand rate is assumed to decrease exponentially. In this study, mathematical models allowing shortage are derived in three different situations, i.e., Case I: The credit period is less than or equal to consumption period for settling the account; Case II: The credit period is greater than consumption period and less than or equal to the cycle time for settling the account; Case III: The credit period is greater than the cycle time for settling the account. Expressions for total cost per time unit of an inventory system are derived on the basis of the above three cases. These models assist the decision-makers in successfully determining the cycle time, shortage time and ordering quantity. A numerical example is given to demonstrate the effectiveness of the derived model.