The Commonwealth Games is an international multi-sport event that takes place every four years and involves athletes from countries that are members of the Commonwealth of Nations. The Commonwealth of Nations is an association of 54 sovereign states, most of which are former territories of the British Empire. While the majority of Commonwealth countries participate in the Commonwealth Games, there are a few countries that do not participate for various reasons.

One country that does not participate in the Commonwealth Games is Rwanda. Rwanda is a landlocked country in East Africa that became a member of the Commonwealth of Nations in 2009. While Rwanda is a member of the Commonwealth, it has never participated in the Commonwealth Games. The reasons for this are not entirely clear, but it is likely due to the fact that Rwanda has a relatively small population and limited resources to support a large-scale sports program.

Another country that does not participate in the Commonwealth Games is Mozambique. Mozambique is a country located in southeastern Africa that gained independence from Portugal in 1975. While Mozambique is a member of the Commonwealth of Nations, it has never participated in the Commonwealth Games. The reasons for this are also not entirely clear, but it is believed that the country's focus on rebuilding after a long civil war has limited its ability to develop a strong sports program.

A third country that does not participate in the Commonwealth Games is Equatorial Guinea. Equatorial Guinea is a small country located in central Africa that gained independence from Spain in 1968. While Equatorial Guinea is not a member of the Commonwealth of Nations, it has been invited to participate in the Commonwealth Games in the past, but has declined the invitation. The reasons for this are not entirely clear, but it is believed that the country's government has prioritized investment in other areas, such as infrastructure and oil production, over sports development.

In conclusion, while the majority of Commonwealth countries participate in the Commonwealth Games, there are a few countries, such as Rwanda, Mozambique, and Equatorial Guinea, that do not participate for various reasons. These reasons range from limited resources to support a sports program to a focus on other areas of development.