The open set In the special bitopological space (X?,??) denoted by ?-open set and the collection of all ?-open sets forms a topological space on X denoted by ?? greater than ? . [N.Levine , 1961] introduced the concept of weak continuity as a generalized of continuity , later [Hussain ,1966] introduced almost continuity as another generalization and [Anderew and whitlesy , 1966]introduced the concept of closure continuity which is stronger than weak continuity .[singal and singal , 1968] introduced anew almost continuity which is different from that of hussain.the purpose of this paper is to further the study of the concept of strong ?-continuity and almost strongly ?-continuity ,faintly ?-continuity ,and weakly ?-continuity in bitopological spaces. A function f: (X,?,??)?(Y,?,?? )is weakly ?-continuous function at a point x?X if given any ?-open set V in Y containing f(x) ,there exist ?-open set U containing x such that f(U)?cl? (V).if the condition is satisfied at each x?X then f is said to be weakly continuous function. the function f is strongly ?-continuous function at x?X if given any ?-open set V in Y containing f(x) ,there exist ?-open set U containing x such that f(cl?(U)?(V).if the condition is satisfied at each x?X then f is said to be strongly ?-continuous function, and it is called almost ?-continuous if for each point x?X and each ?-open set V in Y containing f(x) there exist ?-open set U in X containing x such that f(U)?int?(cl?(V)) .the function f is said to be almost strongly ?-continuous if and only if for ach x?X and ?-nbd V of f(x) there exist ?-open set U containing x such that f(cl?(U))?int?(cl?(V)). A bitopological space (X,?,??) is called urysohn if for every x?y in X there exist ?-open sets U,V in X such that x?U ,y?V and cl?(U)?cl?(V)=? and if (X,?) is Urysohn space then (X, ?,??) is also urysohn space..