Perturbation methods are used to study the dynamics of locked fluxon m
odes on stacked Josephson junctions and single crystals of certain hig
h-T-c, superconductors. Two limiting cases are considered: (i) The non
linear diffusion regime in which fluxon dynamics are dominated by ener
gy exchange between the bias and loss parameters, and (ii) the propaga
ting regime in which the interplay between magnetic and electric field
energies governs the fluxon dynamics. Conditions for stability of loc
ked fluxon modes are shown to be different in these two regimes.