Nearly all polymers form glasses and the glass transition at temperature Tg dominates many physical properties of polymers that are relevant for their applications. The most detailed previous muon studies of polymer glasses have been made in TF mode using diamagnetic muon probe states. This works particularly well in low Tg systems for probing Tg near the surface of thin films using low energy muons. If Tg approaches or exceeds room temperature then fast diffusion of unbound diamagnetic muons forces a switch to bound paramagnetic muon probe states. LF muSR techniques will be developed here for polymer glass studies using the relaxation of the paramagnetic muons at both low LF and at ALC resonance points to probe the dynamical state of the polymer. The studies will focus on two polymers, the biocompatible polymer poly(L-lactide) (Tg=335K) and the low Tg polymer polybutadiene (Tg=170K)