A contract where only one party makes an express promise or an agreement to perform without receiving or securing a reciprocal promise and where the offeree can later act upon such promise, e.g. a promise to pay another $100 if they refrain from smoking for the next 3 months. civil law. When the party to whom an engagement is made, makes no express agreement on his part, the contract is called unilateral, even in cases where the law attaches certain obligations to his acceptance.