Katydids are members of the grasshopper family, and can be distinguished by their long "horns," bright green color, and by the male's loud, shrill call which sounds like "Katy did" and thus has earned them their onomatopoeic name. They do not pose any particular problem for the home gardener, but do feed on shrub and tree foliage.

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Coneheaded katydid or grasshopper, Neoconocephalus ensiger (Orthoptera)
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Katydid (Orthoptera) eggs on stem
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Katydid (Orthoptera) eggs on stem
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Katydid (Orthoptera) eggs on stem
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Black-legged meadow katydid (Orthoptera) on knockout rose (Rosa 'Radrazz' KNOCK OUT)
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Close-up of black-legged meadow katydid (Orthoptera) on knockout rose (Rosa 'Radrazz' KNOCK OUT)