in civil engineering, deep foundation systems, specifically pile foundations, play a critical role in transferring the structural loads of heavy constructions from superstructures to deeper layers of soil. the consequences of such failures are far-reaching and can incur property damage, structural failure, and tragically, loss of human lives. it is imperative to address the potential risks associated with pile foundation failure, particularly under seismic conditions. conventionally only dynamic forces with a single frequency are investigated. in many cases of civil engineering, however, the dynamic force is not periodic with a single frequency but quasiperiodic with multiple frequencies. while there have been numerous studies on the buckling stability of piles, there is a noticeable scarcity of research that considers the influence of seismic excitations with two frequencies. the primary objective of this research is to study the dynamic stability of pile foundations under seismic excitations with two frequencies analytically and numerically. the study commences by driving the equation of motion for a pile foundation under earthquake, which is decoupled into an ordinary differential equation with variable coefficients of two frequencies. the harmonic balance method is used to analytically construct the stability diagrams of the pile. a numerical method is also presented to study the stability of columns under dynamic loads with two frequencies. the numerical results of instability diagrams can also serve as a calibration of other approximate results. as an application example, the dynamic stability of a real pile foundation is investigated using both the harmonic balance method and the numerical method. this is followed by parametric studies involving factors such as elastic foundation rigidity, damping, and dynamic and static loads on the instability regions. the outcomes of this research carry significant practical implications, particularly in the domain of designing pile foundations for mega-structures. designers can leverage the findings of this study to incorporate the effects of multiple frequencies on pile behavior into their design considerations, thereby enhancing the structural age and safety of constructions.