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In my personal experience NO Staffie's do not drool after long walks over the years i have owned 6 staffies and none of them drooled.
Excessive drooling (ptyalism) is most often a sign of nausea. It can also be a sign of anxiety as someone pointed out earlier, or a sign of oral or dental disease. However, many dental and oral diseases can only be accurately diagnosed when a pet is sedated or under anesthesia, and often require dental x-rays.