whether the private supplementary agreement is valid depends on the specific circumstances. If the contents of the agreement do not violate the mandatory provisions of laws and administrative regulations, and both parties have full capacity for civil conduct, they voluntarily sign and affix their official seals or signatures, then the agreement is valid. However, if the content of the agreement violates the mandatory provisions of laws and administrative regulations, or there is fraud or coercion, then the agreement is invalid.

Private supplementary agreement refers to a written agreement reached by both parties to supplement or modify the original contract terms through consensus during the performance of the contract. The effectiveness of the private supplementary agreement depends on the specific circumstances.

first of all, the private supplementary agreement must comply with the law. If the contents of the agreement violate the mandatory provisions of laws and administrative regulations, then the agreement is invalid. For example, if the two parties agree in a private supplementary agreement that violates national laws and regulations, then the agreement is invalid.

Secondly, both parties must have full capacity for civil conduct. If one party is underage or mentally ill, then the party cannot sign a private supplementary agreement.

thirdly, both parties must voluntarily sign and affix their official seals or signatures. If there is fraud, coercion, etc., then the agreement is invalid. For example, if one party cheats the other party into signing a private supplementary agreement, then the agreement is invalid.

To sum up:

Whether the private supplementary agreement is valid depends on the specific circumstances. If the contents of the agreement do not violate the mandatory provisions of laws and administrative regulations, and both parties have full capacity for civil conduct, they voluntarily sign and affix their official seals or signatures, then the agreement is valid. However, if the content of the agreement violates the mandatory provisions of laws and administrative regulations, or there is fraud or coercion, then the agreement is invalid.

Legal basis:

Article 52 of the Contract Law of the People's Republic of China stipulates: "A contract is invalid under any of the following circumstances: (1) One party enters into a contract by fraud or coercion, which harms the national interests; (two) malicious collusion, damage the interests of the state, the collective or the third party; (3) Covering up illegal purposes in a legal form; (four) damage the interests of the public; (5) Violating the mandatory provisions of laws and administrative regulations. "