On 27 May 1975, President Kenneth Kaunda named Mudenda as the Prime Minister after Mainza Chona resigned.
Mudenda was given the overall responsibility of running all of the ministries concerned with the economy in an attempt to stimulate non-mining sectors.
He was removed as Prime Minister on 20 July 1977, and replaced by the same man who held the position two years earlier.
Following his death, Mudenda was given a state funeral and was buried on 6 November 2008, at his Sun Valley farm, located in the New Kasama area of Lusaka.
Indeed, a vision for the advancement and prosperity of our beloved continent", and he stated that Mudenda would have a lasting legacy.