The Collaborative International Dictionary of English v.0.48:

Besiege \Be*siege"\, v. t. [imp. & p. p. Besieged; p. pr. &
   vb. n. Besieging.] [OE. bisegen; pref. be- + segen to
   siege. See Siege.]
   To beset or surround with armed forces, for the purpose of
   compelling to surrender; to lay siege to; to beleaguer; to
   beset.
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         Till Paris was besieged, famished, and lost. --Shak.
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   Syn: To environ; hem in; invest; encompass.
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The Collaborative International Dictionary of English v.0.48:

Besieging \Be*sie"ging\, a.
   That besieges; laying siege to. -- Be*sie"ging*ly, adv.
   [1913 Webster]

WordNet (r) 3.0 (2006):

besieging
    n 1: the action of an armed force that surrounds a fortified
         place and isolates it while continuing to attack [syn:
         siege, besieging, beleaguering, military blockade]