The authors derive conditions for the existence of one-parameter families of periodic solutions for a class of non-smooth coupled systems of second order differential equations. Explicit existence conditions of one-parameter families of periodic orbits for models involving two coupled relay systems are given. The family considered is \[ Z_{(\alpha,\beta,\lambda)}=x_2 \dfrac{\partial}{\partial x_1}+(\alpha\cdot \mathrm{sgn}(x_1)+\lambda y_1) \dfrac{\partial}{\partial x_2}+y_2 \dfrac{\partial}{\partial y_1}+ \beta\cdot \mathrm{sgn}(y_1)\dfrac{\partial}{\partial y_2} \]
with \(\lambda\) as the coupling parameter. This family is perturbed in the following way: \[ Z^*_{(\alpha,\beta,\lambda)}=Z_{(\alpha,\beta,\lambda)}+f_x(x_1,x_2,y_1,y_2) \dfrac{\partial}{\partial x_2}+f_y(x_1,x_2,y_1,y_2) \dfrac{\partial}{\partial y_2}, \]
where \(f_x,f_y\) are analytic functions with null linear parts with the symmetry condition \[ f_\nu(x_1,x_2,y_1,y_2)=-f_\nu(-x_1,x_2,-y_1,y_2). \] The main results show that under some general conditions, the family \(Z_{(\alpha,\beta,\lambda)}\) has a 1-parameter family of periodic orbits, and the perturbed family \(Z^*_{(\alpha,\beta,\lambda)}\) has two families of 1-parameter periodic orbits.