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We have successfully fabricated single-filament composite MgB2/Stainless-Steel (SS) tapes using powder-in-tube processes such as swaging and cold rolling. The transport critical currents, that were measured by a standard dc four-probe method, Ic∼316 A and ∼105 A were observed at T=4.2 K with H=0 G for as-rolled and sintered MgB2/SS tapes, respectively. In addition, the isothermal magnetizations M(H) of sintered MgB2/SS tapes and commercial MgB2 powder were measured at temperatures T between 5 and 50 K in fields up to 6 T, employing a PPMS. The critical current density (Jc) values obtained from the M(H) data, using Bean model, were >5 × 105 A/cm2 and >5 × 107 A/cm2 at T=10 K with H=0 G for the sintered MgB2/SS tapes and the commercial MgB2 powder, respectively. On the other hand, we investigated the cross sections of both the sintered and the as-rolled tapes, using SEM and EPMA. No evidence of significant diffusion between MgB2 and SS tube was found in the SEM/EPMA. However, traces of reaction can be seen in the interface region between MgB2 core and SS tube for the sintered MgB2/SS tapes, from the EPMA line profiles. In addition, impurity phases such as MgO or MgB4, which can be generated inside the superconductor MgB2 core during fabrication, were observed by XRD analyses.