Inheritance relations with a foreign element(s) are a part of civil relations with a foreign element(s) and are governed by Vietnamese private international law. This article aims to introduce the general principle and its supporting principles in the choice-of-law rules applicable to inheritance relations with a foreign element(s) under the private international law of Vietnam. In addition, the authors also look into the relevant regulations in the Law of the People’s Republic of China on the Law applicable to Foreign-related civil relations and the most recent draft of Private International Law of Indonesia3 to review the trend of national laws concerning matters of inheritance relations involving foreign element(s). Based on that analysis, the authors point out some inadequacies in Vietnamese private international law on matters such as the unclear scope of exercising inheritance rights on immovable assets and the uncertain meaning of the rule to choose “law of the closest connection” as the applicable law. With regard to the first question, the authors suggest that the exercise of inheritance rights over immovable properties should only be considered after a person has inherited the estate, thus he becomes the owner of the property and exercises his rights related to the property. In reference to the second question, it is suggested that the “law of the closest connection” should be the law of the country where the immovable property is located; however, if the estate does not include any immovable property, the “law of the closest connection” is the law of the country where all or most of the property is situated.