A weakly nonlinear time dependent theory for the evolution of superharmonics generated by the nonlinear self-interaction of a mode-1 internal tide in non-uniform stratification is developed and compared to numerical simulations. The forcing by the internal tide is found to excite near-pure mode-1 superharmonics whose natural frequency is moder- ately di#erent from twice the internal tide frequency. Consequently, the superharmonics undergo a slow periodic growth and decay that is comparable to an acoustic `beat'. At low latitudes the beat frequency is smaller and the superharmonics can grow to larger amplitude allowing for the possibility of a superharmonic cascade.