The ℓ0-Least Mean Squares (ℓ0-LMS) and ℓ0-Normalized LMS (ℓ0-NLMS) are arguably the best among gradient adaptive algorithms for sparse system identification. However, due to the non-linear and non-convex sparse penalty term in their cost functions, deriving analytical modals for the Mean Square Deviation (MSD) update equation is quiet challenging. In this paper, the significant and zero taps misalignment is studied separately, and then joined in a dynamical manner. Thus, we propose the MSD update equations for both ℓ0-LMS and ℓ0-NLMS, with reasonable assumptions for white input signal. Moreover, the steady state MSD of both algorithms is presented. Simulation results illustrate strong agreement between the derived analytical modals and the empirical simulation.