To clear your searches you just click the x beside the search you want to clear, above the search window.

If you mean the search history. It is cleared every time you shut limewire down. You can also go to Tools>Options>View>Autocompletion, and untick the box by "Enable Autocompletion of Text Fields", click "apply". This will disable the search history function.

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If it ain't broke, fix it till it is!