This paper studies nonlocal morphological operators.Following the strategy proposed for the Nonlocal meansfilter, these operators are based on a local and adaptivedefinition of the structuring element which is specified bysearching for patches in the image that are similar to the onesurrounding the pixel being filtered. After presenting thebasic nonlocal morphological operators using generic structuring elements, we study their robustness in the presence of noise. Then, we illustrate the interest of some nonlocal morphological operators using flat structuring elements for denoising.