This Master's Degree Thesis investigates periodic solutions to nonlinear equations involving integro-dierential operators. We show the existence and we describe these solutions for generalized Benjamin-Ono type nonlinearities, using a variational formulation and a constrained minimization argument. We show that there exists a minimal period for which nontrivial solutions exist, and we also provide stability and qualitative properties of these solutions. Furthermore, in the case of the fractional Laplacian and with suitable exponents of the nonlinearity, we prove that the period where constrained minimizers change from constant to nonconstant is strictly smaller than the period for which the unique positive constant solution loses stability. Within the literature, the articles [5, 10], which concern two problems closely related to ours, claimed that these two values of the period coincide. Their arguments to prove such claim were incomplete but, if they could be completed, they would also work for our equation. In this work we show that this task cannot be carried out, since we nd an explicit range of parameters (concerning the fraction of the fractional Laplacian and the pure power in the nonlinearity) for which the equality does not hold.