A subgroup of those patients who are not responsive to analytic treatment, despite meeting the usual criteria of analyzability, is considered. These patients typically have significant addictive, psychosomatic, and post-traumatic problems. They show a characteristic picture, now called "alexithymia." This involves an impairment of the ability to recognize, name, or verbalize emotions. The effects manifest themselves mainly in mixed physiological responses, which call attention to themselves rather than to their meaning or story. These emotions, which are less useable as signals, are dedifferentiated and resomatized. There is also a type of "operative thinking" with marked limitations in wishfulfillment and drive-related fantasy. There is a diminution of symbolization, and with it an impairment in the capacity to elaborate the kind of fantasies that underly neuroses and the related transferences. They also have a seriously diminished emotional involvement with their objects and a lowered capacity for empathy. Lastly, there are frequently associated problems such as anhedonia, impairments in the capacities for self-care, and affect tolerance. The impediments to psychoanalytic treatment resulting from this picture are considered, and some theories of its causation and therapeutic modifications calculated to enable these patients to benefit from psychotherapy are offered.