In this paper we construct a generalized deformed algebra having the q
-deformed Heisenberg-Weyl algebras and Tamm- Dancoff algebra as its sp
ecial cases. We also show that the algebra is a Hopf algebra. Moreover
we obtain a realization of the generalized deformed su(N) algebra in
terms of the generalized deformed Heisenberg-Weyl algebra and discuss
the deformed harmonic oscillator problem.