Abstract: In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the whole real axis. The properties of approximation are studied and their asymptotic formulae are presented. These results show that their degrees of approximation are the best among existing operator sequences of Landau type, for example, their degrees of  approximation for C²[0, 1] are O(1/n²) but corresponding degree of ordinary Landau operators are only O(1/n). 

Key words: generalized Landau linear positive operators, degree of approximation, asymptotic formula