  Hermite processes are self--similar processes with stationary increments
which appear as limits of normalized sums of random variables with long range
dependence. The Hermite process of order $1$ is fractional Brownian motion and
the Hermite process of order $2$ is the Rosenblatt process. We consider here
the sum of two Hermite processes of order $q\geq 1$ and $q+1$ and of different
Hurst parameters. We then study its quadratic variations at different scales.
This is akin to a wavelet decomposition. We study both the cases where the
Hermite processes are dependent and where they are independent. In the
dependent case, we show that the quadratic variation, suitably normalized,
converges either to a normal or to a Rosenblatt distribution, whatever the
order of the original Hermite processes.
