We report 20 cases of a peculiar fatty tumor that occurred in 16 female and four male patients who were 14-70 years old (median, 36 years). Most lesions were situated in the subcutis, superficial muscular fascia, or skeletal muscle of the limbs and limb girdles (15), trunk (3), and the head and neck (2). They were 1.5-11 cm in size (median, 4 cm) and usually described as yellow (13 of 15) and encapsulated (13 of 15). Microscopically they were well circumscribed and consisted of nests, strands, and sheets of eosinophilic and vacuolated cells, which contained glycogen and fat droplets, resembling brown fat cells, lipoblasts and chondroblasts. In all cases there was a variable background of mature adipose tissue associated with a prominent, partially fibrinous to hyalinized myxoid matrix that contained acid mucopolysaccharides usually resistant to hyaluronidase digestion. Several cases had foci of serous atrophy, perivascular fibrosis, and small thrombi; two were focally calcified. The lesions stained for S100 protein (11 of 12), vimentin (10 of 11), and CD68 antigen with KP1 (9 of 11); focal staining for keratin was also seen (4 of 11), but none stained for epithelial membrane antigen or actin or with HMB45. Follow-up in 12 cases (median, 9.5 years) revealed no local recurrences or metastases. Despite its deep location and atypical cellular features, the lesion's nonaggressive behavior suggests it is benign and neither a myxoid liposarcoma nor a myxoid chondrosarcoma, with which it is most frequently confused. The presence of glycogen in vacuolated fat cells is similar to brown fat, and the presence of sulfated stromal mucins supports focal chondroid differentiation. Although the pathogenesis remains uncertain, a lipoma with hibernomatous features, myxoid change, chondroid metaplasia, and secondary degenerative features is favored over a lipogranulomatous process.