Wave propagation is studied in structures consisting of alternate left- and right-handed layers. Bragg gap and zero-n gap appear in different frequency regions of the structure. The periodicity of the structure is broken by simply reversing the order of the layers in one half of the structure, resulting in defect modes located inside the zero-n gap and Bragg gap. These modes can be made very narrow by adding more layers in the structure. The defect mode located inside the zero-n gap is sensitive to the symmetry of the structure and insensitive to the angle ofincidence of the incoming radiation. Multiple modes are also generated inside the gaps by repeating the structural pattern. Thus, a simple structure can be used for single and multiple modes that are important for different applications.