A stochastic process \(\{X_ t:\) \(t\geq 0\}\) on \({\mathbb{R}}^ d\) is called wide-sense self-similar if, for each \(c>0\), there are a positive number a and a function b(t) such that \(\{X_{ct}\}\) and \(\{aX_ t+b(t)\}\) have common finite-dimensional distributions. If \(\{X_ t\}\) is wide-sense self-similar with independent increments, stochastically continuous, and \(X_ 0=const\), then, for every t, the distribution of \(X_ t\) is of class L. Conversely, if \(\mu\) is a distribution of class L, then, for every \(H>0\), there is a unique process \(\{X_ t^{(H)}\}\) self-similar with exponent H with independent increments such that \(X_ 1\) has distribution \(\mu\). Consequences of this characterization are discussed. The properties (finite-dimensional distributions, behaviors for small time, etc.) of the process \(\{X_ t^{(H)}\}\) (called the process of class L with exponent H induced by \(\mu\)) are compared with those of the Lévy process \(\{Y_ t\}\) such that \(Y_ 1\) has distribution \(\mu\). Results are generalized to operator-self-similar processes and distributions of class OL. A process \(\{X_ t\}\) on \({\mathbb{R}}^ d\) is called wide-sense operator-self-similar if, for each \(c>0\), there are a linear operator \(A_ c\) and a function \(b_ c(t)\) such that \(\{X_{ct}\}\) and \(\{A_ cX_ t+b_ c(t)\}\) have common finite- dimensional distributions. It is proved that, if \(\{X_ t\}\) is wide- sense operator-self-similar and stochastically continuous, then the \(A_ c\) can be chosen as \(A_ c=c^ Q\) with a linear operator Q with some special spectral properties. This is an extension of a theorem of W. N. Hudson and J. D. Mason [Trans. Am. Math. Soc. 273, 281-297 (1982; Zbl 0508.60044)].