We have developed thin film amorphous silicon alloy (a-Si:H) and nanocrystalline silicon (nc-Si:H) based multijunction solar cells on lightweight polymer substrate ~25 μm thick for space and near-space applications. The baseline cells use an a-Si:H/a-SiGe:H/a-SiGe:H structure deposited by conventional Radio Frequency (RF) plasma enhanced CVD using roll-to-roll deposition. The best initial performance for the baseline cells is aperture-area efficiency 9.84% and specific power ~1200 W/kg. The baseline cells are available to potential customers in large quantities. In order to increase the solar cell efficiency, we have pursued two new approaches. In the first, we use a Modified Very High Frequency (MVHF) technique to deposit the multijunction a-SiGe:H based cells. In the second, we have investigated nc-Si:H based multijunction cells. In this paper, we present the solar cell efficiency results on the three different device structures.