In this paper we discuss the role of anharmonicity of lattice waves in electronic specific heat of metals and insulators at very low temperatures. Previous researchers have revealed the anharmonicity of the lattice waves to cause deviation in specific heat from Debye T3 law. Different researchers have given different concepts of anharmonicity in electronic specific heat of metals at very low temperatures. The energy spectrum of phonons can not be fully described by the Debye law. On the whole all reports dilute the contention of the electronic contribution to be responsible for linear temperature dependent component of specific heat of metals at very low temperatures. For anharmonicity of lattice waves this contribution must be expected for metals and insulators also.