Final answer:
Promissory estoppel and contracts under seal are exceptions to the common law rule requiring consideration in contracts.
Step-by-step explanation:
Two exceptions to the common law rule requiring consideration in contracts are promissory estoppel and contracts under seal. Promissory estoppel occurs when a promise is made and the relying party suffers a detriment as a result of relying on that promise. Contracts under seal are written agreements that are signed, sealed, and delivered, and are enforceable even without consideration.