The centered Gaussian process \(X(t),t\in\mathbb{R}\) is called a cyclo-stationary with period \(\tau>0\) if for every \(s\in\mathbb{R}\) its covariance function \(r(t,t+s)=\mathbb{E}\left\{ X(t)X(t+s)\right\} \) is a periodic function with respect to \(t\) with period \(\tau\).Consider cyclo-stationary \(\chi\)-processes defined by \[ \chi_{n}(t)=\left( X_{1}^{2}(t)+\dots+X_{n}^{2}(t)\right) ^{1/2},t\geq0, \] where \(X_{1}(t),\dots,X_{n}(t),t\geq0\) are indepedent copies of a centered cyclo-stationary Gaussian process \(X(t),t\geq0.\) The authors introduce strongly dependent cyclo-stationary \(\chi\)-processes and they obtain limit theorems of the maximum of such processes to some mixed Gumbel laws. Finally, under a global Hölder condition they show that Seleznjev \({p}\)th-mean convergence theorem holds.