All nonexpanding gravitational waves in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math>-dimensional (anti–)de Sitter space

We present a complete, theory-independent classification of $D$-dimensional Kundt spacetimes of Weyl and traceless-Ricci type N. We show that these geometries consist of three invariantly defined subfamilies, namely (generalized) Kundt, pp-, and Siklos waves, for each of which we obtain a convenient canonical form. As a byproduct, this also demonstrates that such metrics coincide with the class of nonexpanding (A)dS-Kerr-Schild spacetimes. The role of these spacetimes in Einstein's gravity (including minimally coupled $p$-forms and nonlinear electrodynamics) as nonexpanding gravitational waves in an (anti)-de Sitter background is discussed. Furthermore, applications to extended theories such as Gauss-Bonnet, Lovelock, quadratic, and $f(R)$ gravity are also briefly illustrated, as well as the overlap of the obtained metrics with universal and almost-universal spacetimes. In the appendixes we additionally settle the issue of the redundancy of certain field equations for all Kundt spacetimes in a theory-independent way and present various alternative coordinates for the spacetimes studied in the paper.