The molecular dynamics of poly(1-trimethylsilyl-1-propyne) in the presence of N2, CO2, CH4 and C2H4, is assessed in situ with broadband dielectric and solid state NMR spectroscopies. The measurements of the dielectric permittivity and the analysis of the dielectric spectra show two secondary β relaxations and the absence of a glass transition. These relaxations could be associated to highly flexible and disordered regions (β1), and to more rigid and ordered ones (β2). The Ea of β1 observed in the presence of CO2 was the highest among the four gases studied, suggesting an increased presence in disordered regions. The results of 13C T1 NMR relaxation measurements provide complementary information on the polymer backbone dynamics. The T1s of main chain carbons increase as the concentration of gas sorbed in the polymer increases, indicative of a decrease in chain mobility. The combination of both spectroscopies afforded additional insight toward the understanding of gas transport in glassy microporous polymers.