The paper examines ways in which strange events, characters and details are described in dream reports. The author analyzes methods of constructing “strangeness” in dream narratives and compares them with the ones which are common in reports on extraordinary and paranormal events. It is demonstrated that several devices which include so-called “contrast structures” and “X-Y structures” might be employed in dream reports. X-Y structures provide mundane contrasts to extraordinary events, while contrast structures juxtapose wrong actions with descriptions of appropriate behavior. So, by applying the opposition of appropriate and inappropriate, and the opposition of extraordinary and mundane, these devices help to portray events as strange. Though these techniques might be used in dream reports, they could also be employed in other narratives, including reports on paranormal experiences or descriptions of behavior of mentally ill people. Their functions in various types of reports are similar; however, the use of these devices in dream narratives is substantially different in some respects. While reports on waking reality juxtapose normal and strange or fitting and wrong, dream reports juxtapose strange elements of a dream with the same elements as if they normally were in reality. Thus, in dream reports the opposition of normal and strange is closely connected with the opposition of waking reality and the dream.