In this talk we discuss the hybridizable discontinuous Galerkin (HDG) methods for the Helmholtz equation with _rst order absorbing boundary condition in two and three dimensions. We prove that the proposed HDG methods are stable (hence well-posed) without any mesh constraint. The stability constant is independent of the polynomial degree. By using a projection-based error analysis, we also derive the error estimates in L2 norm for piecewise polynomial spaces with arbitrary degree.This is joint work with Wujun Zhang from University of Maryland.