We study the delocalization properties of the resonant extended states
in the random dimer model (RDM) with various perturbations added. The
divergent localization length xi is found to display a power-law deca
y xi proportional to W--alpha as a Function of the disorder W in the d
imer or the background energies, with an exponent alpha around 2 depen
ding on the location of the resonant state. For randomness in the dime
r structure the exponent becomes alpha(p) = 1 and for the case of an a
pplied electric field it reaches higher values alpha(e) > 2. These eff
ects on the resonant states are discussed in connection with the elect
ronic transport properties of realistic disordered systems.