In this study, the free flexural (or bending) vibration response of composite base-plate or panel systems stiffened by two adhesively bonded plate strips are theoretically analyzed in detail and numerically solved in terms of the mode shapes with their natural frequencies. Additionally, some important parametric studies are also included in the present study. The aforementioned bonded and stiffened system is composed of an orthotropic Mindlin base plate or panel stiffened or reinforced by the dissimilar, orthotropic two-bonded stiffened-plate strips. The two relatively thin, in-between adhesive layers are assumed as the linearly elastic continua with dissimilar material properties. The plate elements of the system are analyzed in terms of the Mindlin plate theory, which takes into account the transverse (or bending) and the rotatory moments of inertia as well as the normal and the transverse shear deformations. The dynamic equations of each plate element of the system are combined together with the stress resultant displacement expressions and, where appropriate, with the adhesive-layer equations. After some manipulations and combinations, the aforementioned dynamic equations are finally reduced to a new set of the governing system of the first-order ordinary differential equations in the state vector forms. These equations are numerically integrated by means of the modified transfer matrix method (with interpolation polynomials). In the numerical results, the mode shapes with their natural frequencies, up to the sixth mode, are graphically presented, for various sets of the boundary conditions. The significant effects of some of the important parameters, such as the aspect ratio, the stiffener length (or width) ratio, and the bending stiffness ratio on the natural frequencies, are studied and presented up to the sixth mode for several sets of the support conditions. The serious influence of the adhesive-layer material characteristics on the mode shapes and on the natural frequencies in terms of the hard (or relatively still) and the soft (or relatively flexible) adhesive layers are also investigated and are shown for the various sets of the support conditions. Furthermore, some very important conclusions related to the analysis and the design of such bonded and stiffened systems are presented.