<p>In this paper, we develop a theory of Lyapunov exponents for linear singular difference equations (LSDEs), generalizing well-known notions and results in the theory of linear ordinary differential equations and linear difference equations. We begin by addressing the solvability of LSDEs in their strangeness-free form, laying the foundation for the subsequent introduction of Lyapunov exponents and the Lyapunov spectrum. Key properties of Lyapunov exponents are explored, including their relationship with the Lyapunov exponents of the associated underlying difference equations and the regularity in Lyapunov’s sense. Additionally, adjoint systems are introduced, and their properties are analyzed. Finally, we establish a necessary and sufficient condition for the stability of Lyapunov exponents with respect to perturbations in the coefficients of LSDEs.</p>