  In the context of Two Time Physics in 4+2 dimensions we construct the most
general N=2,4 supersymmetric Yang Mills gauge theories for any gauge group G.
This builds on our previous work for N=1 supersymmetry. The action, the
conserved SUSY currents, and the off-shell SU(N) covariant SUSY transformation
laws are presented for both N=2 and N=4. The on-shell SUSY transformations
close to the supergroup SU(2,2$|$N) with N=1,2,4. The SU(2,2)=SO(4,2)
sub-symmetry is realized linearly on 4+2 dimensional flat spacetime. All
fields, including vectors and spinors, are in 4+2 dimensions. The extra gauge
symmetries in 2T field theory, together with the kinematic constraints that
follow from the action, remove all the ghosts to give a unitary theory. By
choosing gauges and solving the kinematic equations, the 2T field theory in 4+2
flat spacetime can be reduced to various shadows in various 3+1 dimensional
(generally curved) spacetimes. These shadows are related to each other by
dualities. The conformal shadows of our theories in flat 3+1 dimensions
coincide with the well known counterpart N=1,2,4 supersymmetric massless
renormalizable field theories in 3+1 dimensions. It is expected that our more
symmetric new structures in 4+2 spacetime may be useful for non-perturbative or
exact solutions of these theories.
