The visual system has to segregate objects that are relevant to behavior from other objects and the background, if they are embedded in a visual scene. This segregation process can be time consuming, especially if the relevant object is spatially extended and overlaps with other image components, but the cause of the delays is presently not well understood. In the present study, we used a curve-tracing task to investigate processing delays during the grouping of contour segments into elongated curves. Our results indicate that contour segments that need to be grouped together are labeled with visual attention. Attention gradually spreads from contour segments that were labeled previously to other contours that are colinear and connected to them. The contour-grouping task is completed as soon as attention is directed to the entire curve. We conclude that processing delays during contour grouping are caused by a time-consuming spread of visual attention.