The evidence supporting Vietnam's claim over these territories includes:

### 1. *Historical Evidence*:

* *Historical Documents*: Vietnam has historical records dating back to the 17th century, showing that the Vietnamese rulers governed and administered the Hoàng Sa and Trường Sa archipelagos. These records include maps, documents, and even reports from Western sailors and explorers in the region.

  * In particular, Vietnamese emperors, notably those from the Nguyễn dynasty (1802–1945), issued several official documents that clearly affirm Vietnam’s control over the islands. For example, the "Gia Long edict" (1816) and various decrees issued by Emperor Gia Long (1802-1820) established Vietnam’s administrative jurisdiction over both archipelagos.
* *Chinese and Western Records*: Historical records from both Chinese and Western sources also mention Vietnamese presence in the islands. For instance, early Chinese records indicate that Vietnamese fishermen used the islands as fishing grounds and navigational references well before the Qing Dynasty's claims in the 20th century.

### 2. *Legal Evidence*:

* *International Treaties*: Vietnam’s claim is further supported by international treaties signed in the 19th and 20th centuries. Notably, the 1884 Treaty of Huế between France (representing Vietnam) and China, which affirmed Vietnam’s sovereignty over these territories at the time of French colonial rule.

* *Post-World War II Documents*: After the end of WWII, Vietnam reaffirmed its sovereignty over the islands. In the 1951 San Francisco Peace Conference, the Treaty of Peace with Japan was signed, and the islands were considered part of the territories to be returned to Vietnam, as Vietnam was one of the Allied nations.

* *International Recognition*: Several international organizations and countries, including France, the United States, and the Philippines, have recognized Vietnam's sovereignty over these islands in various forms.

### 3. *Geopolitical Evidence*:

* *Vietnam’s Administrative Control*: Vietnam has maintained continuous administrative control over the islands. It has established government posts, lighthouses, and other infrastructure on both the Hoàng Sa and Trường Sa islands.

* *Military and Civil Presence*: Vietnamese forces have been stationed in these areas for decades, further reinforcing the claim of sovereignty.

### 4. *Modern Legal and Diplomatic Engagement*:

* *United Nations and International Law*: Vietnam has consistently maintained its position on the sovereignty of Hoàng Sa and Trường Sa in international forums such as the United Nations and the Association of Southeast Asian Nations (ASEAN). Under the United Nations Convention on the Law of the Sea (UNCLOS), Vietnam has legal grounds to assert its rights over these islands due to its proximity and historical ties..

Vietnam’s claim is bolstered by a mix of historical documents, treaties, administrative actions, and ongoing governance of the islands, as well as its position within international law frameworks.