Estes, Wellman & Woolley (1989) have shown that children as young as 3 years of age can distinguish between mental entities such as an image or dream of an object and a real object. Nevertheless, children often show persistent fear of imaginary creatures, particularly monsters (Jersild, 1943). To find out what conception children have of such imaginary creatures, 4‐ and 6‐year‐olds were questioned about three types of item: real items (e.g. a cup), ordinary imagined items (e.g. an image of a cup) and supernatural imagined items (e.g. an image of a monster). In two experiments, both age groups sharply differentiated the real items from both types of imagined item. Despite this apparently firm grasp of the distinction between fantasy and reality, two further experiments showed that 4‐ and 6‐year‐olds are not always certain that a creature that they have imagined cannot become real. Having imagined a creature inside a box, they show apprehension or curiosity about what is inside the box, and often admit to wondering whether the creature is actually inside. The experiments suggest that children systematically distinguish fantasy from reality, but are tempted to believe in the existence of what they have merely imagined.