Unless they are ingeniously trying to get to a socialist utopia via the great Kladderadatsch*, the labelling of the Zimbabwean regime as 'marxist' seems somewhat outdated. What started as a struggle for freedom, independence and 'justice for all', has evolved into oppression, depression and misery. Hopes and ideals have faded into desillusion and despair.
Such ideals have certainly played a part in the life of Simon Chimbetu. Having been active in the struggle in the 1970s (although not as a fighter), he turned to a career in music after independence had been won. In the late 1970s he and his brother Naison had been performing with John Chibadura's Sungura Boys. In the revolutionary vigour that came with independance they founded their own band and named it the Marxist Brothers.
Like other Zimbabwean artists the liberation struggle had shaped Simon's view of life. I gather that many of his songs have politically 'coloured' themes, - although others prefer to think this was only a matter of perception.
He went through a very dark period in the late 1980s/early 1990s. After he and his brother had split up in 1988, the following year he was sentenced to four years imprisonment for his involvement in the theft of a car. While in prison, his wife left him.
He managed to bounce back, however, and he continued his musical career with his new band, the Dendera Kings, named (according to this article) "after the Mozambican camp which the Chimbetu brothers called home during the revolutionary struggle against white settlers in the 1970s".
Dendera was also the name of the farm which the Chimbetu brothers obtained in 2000. They were on the receiving end of ZANU-PF's land reform, which caused so much controversy both in and outside Zimbabwe. Simon was again under attack a few years later, when it was reported that he wasn't paying his farm workers. In general, his support and defense of Mugabe's policies gradually led to Chimbetu falling out of sync with his audience.
Simon Chimbetu died under somewhat mysterious circumstances at the age of 49 on August 14, 2005, in Harare.
A more indepth study of his lyrics can be found in this study, and a rather chaotic entry in the wikipedia can be found here.
As an illustration of his work I am including two albums: the Marxist Brothers's first album "Mwana weDangwe" from 1983 and the cassette version of the 1995 album "Karikoga".
"Mwana weDangwe" 1983
*I'm afraid I can't point you in the direction of an explanation of this bit of Marxíst theory. I have found no useful link...
EDIT June 11, 2013: The links to the cassettes have been updated.