Abstract: The present invention relates to the field of textiles, in particular shape-memory polymeric fibers (SMPF) for textile applications or medical applications where shape fixity and recovery can be kept constant over multiple shape-memory cycles. The present invention relates to a covered shape-memory polymeric fiber (cSMPF) (1) having a core fiber (10) comprising a shape-memory polymer fiber and a substantially unstretchable covering yarn (20) wound around the core fiber (10) in a manner that the maximum engineering strain (?max) of the core shape-memory fiber is reduced to at most the strain at the yield point (?yield) of the uncovered core fiber (10) thus limiting the stretchability or deformation of the core shape-memory fibers and/or textiles and/or fabrics comprising a covered shape-memory fiber during programming or use so as to ensure maximum recoverable strain.