The liability insurance contract has developed in various forms to reduce the liability of offenders and to provide relief for victims(피 해자) in cases of accidents. The liability insurance is a property insurance, indemnity insurance and negative insurance in that the insured is responsible for the damage liability to the third party in the accident covered. Various legal issues may occur from the relations among the insured, the insurer and the victim regarding the liability. One example is the case where the insured(offender) is moneyless. In such cases, the victim cannot be compensated by the offender. In order to prevent situations as such, Clause 2 of Article 724 of the Korean commercial law stipulates the direct claim by the victim, thereby providing protection for the victim. According th the clause, the insurer takes over the liability for damage from the insured in a coexistent manner. The issue of extinctive prescription is also influenced by the way we define the characteristics of damage claim. For damage claim, the 2-year extinctive prescription as in insurance claim should be applied analogically to guarantee safe transaction and to induce swift conclusion. The insurer can oppose the victim using the plea which the insured has against the victim. Also, in the liability insurance contract with the limit of liability, the damage claim by the victim comes before the insurance claim by the insured.