Thanks for the clarification.
1) Non-contractual spouse agreed to contractual liability.
This would arise if the spouse had an agreement his or her husband and wife that he would also be liable for the debt. This could be done though an express written agreement or a verbal agreement with the spouse, that the spouse would also be responsible for a debt to a creditor.
2) Authorized the debt my implication under the laws of agency.
This would occur if the debt that was incurred was incurred in furtherance of the spouse's interests. Most noticeably, would be a situation in which the debtor spouse gave the non-contracting spouse a credit card and he or she made the purchases that created a debt.
Otherwise, it can be argued that if a credit card were used to purchase home necessities, then the debt (at least the portion spent on these necessities) would be considered to be on behalf of the husband and wife of the debtor spouse.
This is the legal definition:
"In law, a relationship in which one party (the agent) acts on behalf of and under the control of another (the principal) in dealing with third parties."
I hope the above information is helpful.
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Thanks and best of luck!