Infundibulocystic basal cell carcinoma was described in 1987 as a new type of basal cell carcinoma with follicular differentiation. A great controversy followed this description, mainly about the malignant or benign character of this neoplasm and the distinction from other tumors with follicular differentiation. We present two new cases of this neoplasm: the first one had the typical features of this entity, except for the absence of stroma; the second one showed in the deep portion basaloid nodules similar to those of a nodular basal cell carcinoma. We review the criteria adduced to establish the malignant character of this neoplasm and conclude that both the nosology and biological behavior of this neoplasm with follicular differentiation remain to be determined.