Thesis advisor: Gabor J. Kalman / Mixtures of charged particles, where the components have different charge numbers (Z_A ), masses (m_A ) and densities (n_A ), with A = 1, 2 denoting the components, occur in Nature in a great variety. To be sure, even the simplest plasmas are necessarily multicomponent systems, consisting of negative and positive charges. This feature is, however, obscured within the centrally important and popular OCP (one component plasma) or jellium models, where the role of one of the components is reduced to providing a neutralizing background. When this background is inert, one is led to the Coulomb OCP model, while when the background is polarizable (such as an electron gas surrounding heavy particles), to a Yukawa OCP (YOCP), with a screened Yukawa potential replacing the Coulomb potential between the dynamically active particles. There are, however situations of physical importance, where the OCP description is inadequate and a genuine two component description of a plasma composed of two species is required. This Thesis focuses on the study of the dynamics of many-body systems consisting of two components of like charges (all the Z_A -s being of the same signature) in a neutralizing background. The methodology is based upon parallel attacks through theoretical analysis and Molecular Dynamics (MD) simulations, the latter yielding the capability of instant verification of the former. The investigation involves the study of the partial (i.e. species by species) structure functions S_AB (k, ω) and current-current correlation functions L_AB (k, ω). The Fluctuation–Dissipation Theorem (FDT) con- nects these quantities to the total and partial response functions χ_AB (k, ω) (matrices in species space), which are instrumental in the description of the collective mode excitations of the system. This analysis has revealed an entirely novel feature: both S_11 (k, ω) and S_22 (k, ω) exhibit very sharp and deep (several orders of magnitude) minima in the strongly coupled liquid phase at robust characteristic frequencies of the system, which are virtually coupling independent. The FDT then demands that these anti-resonances show up as well in the imaginary part of the partial density response function χ_AB (k, ω). Our theoretical analysis, based on the Quasi-Localized Charge Approximation (QLCA), has confirmed that this is indeed the case. These anti-resonant frequencies being related to the dissipative part of the response, require a physical description of the principal source of dissipation. This has been identified as the inter-species momentum transfer, governed by drag between the microscopic current fluctuations of the two species. The description of this effect was incorporatedv in the QLCA formalism, making it possible to derive a closed analytic representation of the fluctuation spectra in the frequency domain of interest and compare them with the results of the MD simulations. Other important novel concepts, such as the idea of coupling dependent effective mass, fast vs. slow sound, the mechanism of tran- sition from short-range to long-range interaction have been identified and analyzed. Furthermore, the investigation of the dynamics has led to the first comprehensive description of the mode structures of classical binary Coulomb and Yukawa mixtures at arbitrary coupling values, which has been a longstanding problem in statistical plasma physics. Focusing on the longitudinal excitations, we describe the transition from weak coupling (where one is acquainted with the RPA result yielding only the single plasmon mode in the Coulomb case or a single acoustic mode in the Yukawa case) to strong coupling, with a doublet of modes that arise from the complex rel- ative motion between the two components, as affected by the interaction with the background. / Thesis (PhD) — Boston College, 2019. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.