Effect of the addition of polymeric fine fibers on the rheological properties is studied employing poly(lactic acid) PLA as a matrix. Fine fibers of poly(butylene terephthalate) PBT, whose melting point is higher than that of PLA, is prepared in a PLA matrix by melt-stretching with rapid cooling. Then, the rheological properties of the composites are evaluated at the temperature between melting points of PLA and PBT. It is found that only 1 wt. % of PBT fibers greatly enhances the elongational viscosity, although shear viscosity is hardly changed. In particular, the composite shows strain-hardening behavior, which has not been detected for polymer composites with rigid fibers. Elastic deformation of network composed of flexible PBT fibers, leading to bending of fibers and/or friction between fibers, will be responsible for the strain-hardening. The marked elasticity is also detected for a composite of silicone oil containing the PBT fine fibers. (C) 2011 The Society of Rheology. [DOI: 10.1122/1.3626414]