In this paper, we introduce the class of [λ, ρ] -continuous functions. First, we investigate some relations between the classes of [ λ1, ρ1] and [λ2,ρ2] -continuous functions for different pairs [λ1,ρ1] , [λ2,ρ2]. Next, we give an equivalent condition for a function in order that it will belong to the discussed class.