If someone signs an instrument as a representative with actual or apparent authority, the represented person is liable for it. UCC § 3-402(a).
If someone signs a check payable from his principal's account, the principal is liable for it. UCC § 3-402(c).
If it's unambiguous that an instrument is signed on behalf of someone else named in the instrument, the representative is not liable. UCC § 3-402(b)(1).
- Otherwise, the representative is liable "to a holder in due course that took the instrument without notice that the representative was not intended to be liable on the instrument. With respect to any other person, the representative is liable on the instrument unless the representative proves that the original parties did not intend the representative to be liable on the instrument." UCC § 3-402(b)(2).
Another party can sign the front of a note as guarantor to make himself an accommodation party, making himself liable for the note as well.
If a PETE (person entitled to enforce the note) who is owed money in an instrument does something to compromise the value of the collateral or otherwise does something to contribute to the accommodation party or surety party bearing a loss, the accommodation party is not liable for the amount of the loss.
A PETE has to exhaust his remedies against the primary person before he can go after an accommodation party.