We introduce the notion of upper/lower (Ï„,m)-continuous multifunctions and obtain many characterizations of such multifunctions. The notion of upper/lower (Ï„,m)-continuous mul-tifunctions is a generalization of (Ï„,m)-continuous functions (V. Popa and T. Noiri, Rend Circ. Mat. Palermo (2) 51 (2002), 295-316) and upper/lower ultra continuous multifunc-tions due to Navalagi et al (G. B. Navalagi, M. Lellis Thivagar and R. Raja Rajeswari, Indian J. Math. Comput. Sci. Inform. Techn. 1(1) (2008), 69-74).