The giant muscle protein titin, also called connectin, is responsible for the elasticity of relaxed striated muscle, as well as acting as the molecular scaffold for thick-filament formation(1,2). The titin molecule consists largely of tandem domains of the immunoglobulin and fibronectin-III types, together with specialized binding regions and a putative elastic region, the PEVK domain(3). We have done mechanical experiments on single molecules of titin to determine their visco-elastic properties, using an optical-tweezers technique. On a fast (0.1s) timescale tit in is elastic and force-extension data can be fitted with standard random-coil polymer models, showing that there are two main sources of elasticity : one deriving from the entropy of straightening the molecule; the other consistent with extension of the polypeptide chain in the PEVK region. On a slower timescale and above a certain force threshold, the molecule displays stress-relaxation, which occurs in rapid steps of a few piconewtons, corresponding to yielding of internal structures by about 20 nm. This stress-relaxation probably derives from unfolding of immunoglobulin and fibronectin domains.