Shape memory alloys (SMAs) are well-known as high damping materials. Recently,we have reported that the Cu-Al-Mn SMAs show a high internal friction as well as the other SMAs such as Ni-Ti, Cu-Zn-Al SMAs. Since the Cu-Al-Mn-based SMAs possess an excellent cold-workability, a strong recrystallization texture can be formed by thermomechanical treatment. The present authors demonstrated that the texture control is considerably effective for improving the SM properties and especially, in the Cu-Al-Mn-Ni SMAs with a strong {112}<110> recrystallization texture, a large pseudoelastic (PE) of about 7% can be obtained. Such a texture control is expected to enhance the damping capacity in the Cu-Al-Mn-based SMAs as well as PE. In this study, the effect of texture on the internal friction in Cu-Al-Mn and Cu-Al-Mn-Ni SMAs was investigated by tensile testing mode of Dynamic Mechanical Spectrometer (DMS). In sheet specimens with the {112}<110> texture, value of dynamic damping tanφ depends on the loading direction and an excellent damping capacity of tanφ= 0.1 can be obtained at the rolling direction in the martensite phase condition. Moreover, these Cu-Al-Mn-based SMAs show a high tensile strength over 600 MPa in the martensite phase. The present Cu-Al-Mn-based SMAs should have a great potential as the damping materials. Recently, we have reported that the Cu-Al-Mn SMAs show a high internal friction as well as the other SMAs such as Ni-Ti, Cu-Zn-Al Since the Cu-Al-Mn-based SMAs possess an excellent cold-workability, a strong recrystallization texture can be formed by thermomechanical treatment. The present authors demonstrated that the texture control is quite effective for improving the SM properties and especially, in The Cu-Al-Mn-Ni SMAs with a strong {112} <110> recrystallization texture, a large pseudoelastic (PE) of about 7% can be obtained. Such a texture control is expected to enhance the damping capacity in the Cu- Al-Mn-based SMAs as well as PE. In this study, the effect of texture on the internal friction in Cu-Al-Mn and Cu-Al-Mn-Ni SMAs was investigated by tensile testing mode of Dynamic Mechanical Spectrometer (DMS ). In sheet specimens with the {112} <110> texture, value of dynamic damping tanφ depends on the lo ading direction and an excellent damping capacity of tanφ = 0.1 can be obtained at the rolling direction in the martensite phase. The present Cu-Al-Mn-based SMAs show a high tensile strength over 600 MPa in the martensite phase. The present Cu-Al-Mn-based SMAs should have a great potential as the damping materials.