"In the chapter 1 we will discuss the concentration quenching of luminescence in general. Also we review the basic ytterbium spectroscopy, as well as cooperative Yb emission. Our experimental observations on the quenching of the IR emission of Yb as well as the visible cooperative photoluminescence are presented. NLGETME and GETME theoretical models are developed in chapter 2, two cases we will be taken, (1) donors and acceptors having two energy levels and (2) donors with two energy levels and acceptors with three energy levels. Resonant and off resonance conditions are discussed. To reduce the complexity of the NLGETME, we propose a linear approach based on the Taylor theorem. In the chapter 3 we present the simulations results using NLGETME and GETME, and we approach the Yb3+ quenching problem by considering the construction of dimers as the quenching centers in nanocrystalline ZrO2:Yb3+. Also we discuss the nanocrystal size and phase effect on Donor and acceptor concentration and effective Donor Life time. In the chapter 4 we present conclusions of this work. We have three notable results, (1) we are able to reproduce concentration quenching of Yb ions using the Yb dimmer approach; (2) the NLGETME simulations and the dimer construction lead to observe the donor lifetime dependence on crystallite size; and (3) the nonresonant energy levels between ions is a important parameter that could become an important issue for high concentrations of dopants. At the end of Chapter 4 we indicate some of the immediate perspectives for the continuity of the present work."