1. General: An obligation that cannot be outsourced to a third party according to the terms of the contract. In the event that it is delegated, the second party reserves the right to reject the performance of the obligation. 2. Contracts: The fulfillment of an obligation which is solely the responsibility of the obligatory, and which does restrict delegation of the contract to a third party. For example, The safety of the employees is the responsibility of the employer even though a third party was hired to monitor compliance with safety standards.
TLD Example: The refusal of the promoter to accept another band in place of the one he originally hired was supported by the court which ruled the original performers had a non-delegable duty under the contract.