Peripheral papillary adenomas of the lung are uncommon neoplasms (only ten cases have been described so far in the English literature) composed predominantly of type-II pneumocytes and generally considered benign. We describe here two additional cases of this lung tumor. In both cases histological examination revealed an encapsulated papillary neoplasm with invasion of the capsule and, in one case, invasion of the adjacent alveoli and visceral pleura too. The proliferative index (Ki67) was less than 2% and the epithelial cells were positive for cytokeratins, surfactant apoproteins (SP), and nuclear thyroid transcription factor-1 (TTF-1). Ultrastructurally, the epithelial cells showed the characteristic surface microvilli and cytoplasmic lamellar inclusions of type-II cells. Review of the literature has revealed two other cases of peripheral papillary adenoma of type-II pneumocytes with infiltrative features. Thus, we propose replacing the term peripheral papillary adenoma with peripheral papillary tumor of undetermined malignant potential.