The countries which lie on either side of the Durand Line are Afghanistan and Pakistan.

Explanation:
The Durand Line is a 2,640 km (1,640 mile) long border that separates Afghanistan and Pakistan. It was established in 1893 by Sir Mortimer Durand, a British diplomat, during the rule of the British Raj in India. The line was drawn to demarcate the boundaries of Afghanistan and the British Indian territories, now known as Pakistan.

Here is a detailed explanation of the countries that lie on either side of the Durand Line:

1. Afghanistan:
Afghanistan is a landlocked country located in South Asia. It shares its border with several countries, including Pakistan to the east. The Durand Line forms the eastern border of Afghanistan. The country is known for its diverse culture, rugged terrain, and rich history.

2. Pakistan:
Pakistan is a country located in South Asia. It shares its borders with several countries, including Afghanistan to the west. The Durand Line forms the western border of Pakistan. The country is known for its diverse culture, historical landmarks, and natural beauty.

Significance of the Durand Line:
The Durand Line has been a source of controversy and disputes between Afghanistan and Pakistan. Afghanistan does not officially recognize the Durand Line as the international border, and it claims some of the territories that lie within Pakistan. This border issue has caused tensions and conflicts between the two countries throughout history.

In conclusion, the countries which lie on either side of the Durand Line are Afghanistan and Pakistan. The Durand Line serves as the border between these two neighboring countries, although it has been a subject of dispute and controversy.