In this paper, we introduce neutrosophic upper and neutrosophic lower almost pre-continuous-multifunctions as a generalization of neutrosophic multifunctions. Some characterizations and several properties concerning neutrosophic upper and neutrosophic lower almost pre-continuous- multifunctions are obtained. further characterizations and several properties concerning neutrosophic upper (lower) pre-continuous continuous multifunctions are obtained. The relationship between these multifunctions and their graphs are investigated.