Chitemene slash-and-burn cultivation continues to be a dominating cropping system in northern Zambia even after the introduction of modern technologies such as hybrid maize and fertilizer. The rationale of farming systems evolution in northern Zambia where labour markets have been absent or highly imperfect, has been analyzed by goal programming based on the theories of Chayanov (1966) and Nakajima (1986). Carrying capacity estimation is incorporated in the models and discussed in relation to the sustainability of land use systems in the area. The major changes in agricultural technologies in northern Zambia during this century has been the introduction of cassava, maize and fertilizer technologies. Cassava has had the most significant impact since the land could support much higher population densities and since the dependence on the chitemene system no longer was critical for the survival of peasants. By switching from finger-millet to cassava as the main staple the peasants could reduce their total labour requirement to meet their basic food needs by as much as 40%. The results also show that the maize-fertilizer technology has been unable to replace the chitemene system because economic incentives to continue the system exist as long as there is suitable woodland available. Nevertheless, the introduction of the maize-fertilizer technology may have resulted in reduced chitemene cultivation. The rapid expansion of maize production in northern Zambia from the late 70s to the late 80s depended critically on the government policy of equity pricing and input subsidisation. The models predicted that the removal of fertilizer subsidies would result in a dramatic reduction in maize production.