Wet-spun stimuli-responsive composite fibers made of covalently crosslinked alginate with a high concentration of single-walled carbon nanotubes (SWCNTs) are electroconductive and sensitive to humidity, pH, and ionic strength, due to pH-tunable water absorbing properties of the covalently crosslinked alginate. The conductivity depends on the material swelling in humid atmosphere and aqueous solutions: the greater the swelling, the smaller is the electrical conductivity. The covalently crosslinked fibers reversibly deform during the swelling/shrinking. In the swollen state, the fibers are less conductive, while they return to the same level of conductivity after shrinking. This unique reversible change of electroconductivity of the SWCNT-alginate fibers is due to the elastic deformation of the alginate network in the area of electrical contacts between SWCNT bundles arrested in the alginate matrix. Fibers of this kind can be used as a simple, robust, disposable, and biocompatible platform for electrotextiles, biosensors, and flexible electronics in biomedical and biotechnological applications.