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Ned Shimmelfinney is Doc's neighbor, sometimes friend and sometimes rival on Fraggle Rock. Ned has a cat named Fluffinella. Over the course of the series, despite their spats and disagreements, Doc and Sprocket develop a close relationship with Ned, which becomes significant in the final episodes.

Ned Shimmelfinney is referred to often, but never fully seen onscreen. Sprocket frequently does an imitation of Ned, involving gurgling noises and distorted face and hand waving, and Doc once remarked on his penchant for wearing green argyle sweaters. The only physical glimpse the audience has of Ned is a single hand in "The Finger of Light," handing Doc a neighborhood petition through the door.

In "Inspector Red," Doc first learns of Ned's illness. Ned has to move to the desert for his health in "Change of Address," taking Fluffinella with him. Doc and Sprocket make the weighty decision to move as well, in order to be with Ned.