For interconnected systems of the type \[ \dot x_i= f(x_i, x_{i- 1},\dots, x_{i- r+ 1}),\tag{1} \] \(i\in \mathbb{N}\), \(x_i\equiv 0 \forall i\leq i_0\) with some fixed \(i_0\), where \(x_i\in \mathbb{R}^n\), \(f: (\mathbb{R}^n)^r\to \mathbb{R}^n\), \(f(0, \dots, 0)= 0\), the authors introduce the notion of string stability. They derive sufficient (``weak coupling'') conditions which guarantee the asymptotic string stability of a class of systems (1), and they show that under the same conditions string-stable interconnected systems remain string-stable in the presence of small structural or singular perturbations. The authors discuss direct adaptive control of such interconnected systems, and they provide an example of longitudinal controller design for vehicle-following systems.