Rhodesia was a democratic nation in the sense that it had the Westminster parliamentary system with multiple political parties contesting the seats in parliament, but as the voting was dominated by the White settler minority and that the Black Africans only had a minority level of representation at that time (17 seats as opposed to 50 seats for the whites), it was regarded as a racist state internationally.
Rhodesian Prime Minister Ian Smith wanted to gradually include the Black Rhodesians in the political process over a period of years as the rapid granting of independence to other former British, French, and Belgium colonies was proving to be a disaster (one-party states, factionalism, and Marxist ideology), but Great Britain wanted Rhodesia to speed up the process regardless of the consequences. Britain was being pushed by the OAU to do so, but Rhodesia resisted, finally declaring independence in 1965.
Thoughout its period of independence, the Westminster parliamentary system was retained, though the imposing of a State of Emergency as the result of increasing guerilla warfare did curb a number of freedoms. The Prime Minister retained administrative power of the country while ceremonial power went first to an 'Officer Administering the Government', then later a President when Rhodesia became a republic in 1970.
The political party that held sway throughout the UDI years was the Rhodesian Front. Ian Smith remained Prime Minister right up to the end of Rhodesia in 1979.