In a linear differential equation of a vibrating string there is a link representing stiffness of the string. In nonlinear theory, string stiffness has not yet been taken into consideration. The author has completed this by means of the Lagrange II method and presents essential results. The significance of string stiffness is different for the different groups of instruments. Pianos have remarkably stiff strings. This is inevitable and also necessary because stiffness participates essentially in forming vividness of sound. The well-known ‘‘stretched octaves’’ and also the typical tuning curve are caused by this. For plucked strings, stiffness forms character of sound, together with choice of plucking spot on string and with corpus. For bowed strings, it is preferable to have strings, with minor stiffness, because the interaction of bow/string is better. The effects of jitter and rippling (supplement of sound with statistic noise effects) are better formed by less stiff strings. For wound strings, minor stiffness is possible with cores of filament structure. Theory and examples will be discussed. a)Present address: Erich Ohser Str. 10, D-08525 Plauen, Germany.