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On the basis of the two-dimensional numerical simulation the isothermal current instability and filamentation are studied in the grounded gate MOS ESD protection (ggMOS) structures with lightly doped drain (LDD). It is demonstrated that avalanche injection breakdown in the LDD MOS structures results in two stage secondary breakdown and filamentation process. In the first stage a low amplitude filament limited by current saturation in LDD region is formed. In the second stage high amplitude filaments are formed between the source and drain contact n+-regions. The local burnout of the structure is clarified by the resulting high local overheating in the isothermal filament.