Cognition-related brain responses to meaningful and meaningless figures were registered in 5-year-old kindergarten children who either had been subtyped as being at-risk of developing an L- or P-type dyslexia (LAL versus LAP) or who were not at-risk. While identifying, naming, or categorizing pictures, event-related potentials (ERP) were registered. Three cognition-related components were found: the N460, the P780, and the Slow Wave (SW). LAP-children produced weak N460 activity across tasks, whereas LAL children, and to a lesser degree, non-risk children produced robust task-dependent activity. This finding may indicate that LAP-children lack semantic input while processing the figures. P780 latencies to frequently occurring figures were found hemisphere-dependent: LAP-children showed longer latencies in the right than in the left hemisphere, whereas the distribution was reversed in the LAL and non-risk children. It was also found that the right hemisphere is generally responsible for a lion's share of the processing of figures and therefore it seems that the right hemisphere of LAP-children invests ample time in doing so. Whereas LAP-children showed largest SW amplitude differences between frequent and infrequent stimuli at posterior locations, LAL children did so at frontal locations. Assuming that the SW represents working-memory processes, it may be that working-memory in LAP-children deals with figure-relevant visual-spatial information and with figure-derived concepts in LAL children. Overall, the findings suggest that LAL and LAP represent two different groups of kindergartners at risk of dyslexia and that these differences, to some degree, fit with the presumed etiology of L- and P-type dyslexia.