We present two cases, one of a gastrointestinal stromal tumor (GIST) in the stomach and one of an extragastrointestinal stromal tumor (EGIST) in the hepatogastric ligament, which were discovered as incidental findings during computed tomography (CT) scans performed for other reasons. In both cases the diagnosis of the tumor was confirmed histologically and immunohistochemically. During the follow-up CT examinations these tumors proved to have a completely different natural course. The first case refers to an 82-year-old male patient with GIST of the stomach who refused to be operated and was followed by CT scans for a 4-year period. This patient did not show any significant changes in the morphology, size and density of the lesion. The second case refers to a 58-year-old female patient with EGIST of the hepatogastric ligament who presented with simultaneous liver metastases and remained healthy for 2 years after surgical resection, but developed local recurrence later. As a conclusion, both GISTs/EGISTs can be revealed as incidental findings in a CT scan performed for other purposes. Moreover, an untreated GIST located in the stomach can remain unchanged and without metastatic lesions for a long period of time, as in our case for a 4-year period. To our knowledge, this is the first report in the literature in whom a GIST was proved to remain almost unchanged for many years without any treatment, and we therefore attempt a further review of the current literature on stromal tumors.