Given a partial or ordinary differential equation (1)

$f(x,u,{u}_{{x}_{i}},{u}_{{x}_{i}{x}_{j}},\cdots )=0$, a nonlinear superposition principle is a binary operation

$F$ defined on the set of all its solutions. Thus,

$w=F(u,v)$ solves (1) whenever

$u,v$ do. This concept is attributed to

*S. E. Jones* and

*W. F. Ames* [J. Math. Anal. Appl. 17, 484-487 (1967;

Zbl 0145.13201)]. Out of the scope of the present paper are nonlinear superposition principles with restricted domain, such as those resulting from permutability of BĂ¤cklund transformations. Exploiting close similarity to symmetries, applicable techniques to find superposition principles embeddable in a 1-parametric family are suggested that also reveal a linearizing transformation for the equation (1). Presented are classification results for second-order PDEs in two independent variables. The authors also discuss the existence of isolated superposition principles and suggest a method to find them.