We generalize the ideas and formalism of two-time physics from particle dyn
amics to some specific examples of string and p-brane(p greater than or equ
al to 1) dynamics. The two-time string or p-brane action can be gauge fixed
to produce various one-time string or p-brane actions that are dual to eac
h other under gauge transformations. We discuss the particular gauges that
correspond to tensionless strings and p-branes in flat (d - 1) + 1 spacetim
e, rigid strings and p-branes in flat (d - 1) + I spacetime, and tensionles
s strings and p-branes propagating in the AdS(d-n) x S-n backgrounds. (C) 1
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