Experiments are described in which observers attempted to perform concurrently two separate visual tasks. Two types of tasks were used: the identification of a T-shaped or L-shaped letter target, and the detection or localization of a texture element of unique orientation (texture target) within a dense texture. Combining these tasks to form various task pairs, performance as a function of stimulus onset asynchrony (SOA) was established separately for each task in a pair. In addition, performance was measured when each task was carried out by itself. When paired, two identification tasks (T or L) on (two) letter targets required a significantly larger SOA than either identification task by itself. This outcome suggests the involvement of serial performance and competition for a limited resource, confirming that letter identification requires attentive fixation. However, when the identification of a central letter target was paired with the localization (upper or lower hemifield) of an eccentric texture target, performance in the pair was comparable to performance of each task by itself. This suggests parallel performance and a lack of conflict over resources. The outcome was similar when the identification of an eccentric letter target was paired with the detection (present or absent) of an eccentric texture target. These results are consistent with the possibility that localization and detection of a textural singularity do not require attentive fixation.