Closed form, approximate expressions are found for the electromagnetic eigenstates of an isolated, finite-length, circular cylinder, of radius a and length L, for the case where ka ≪ 1 but kL is greater than 1 (k is the wavenumber in the surrounding medium). These eigenstates are standing waves of surface plasmons which propagate along the cylinder axis and are reflected, back and forth, between the cylinder ends. When considering a cluster of such cylinders, the combined set of these non-quasistatic eigenstates, arising from each of the cylinders in isolation, form a set of vector fields that is complete in the quasistatic limit. This basis can be used as a starting point for evaluating the electromagnetic eigenstates of the entire cluster or even of a periodic array of such cylinders when one is close to the static regime. These states are used to develop a systematic calculation of the macroscopic electromagnetic response of a collection of such cylinders. Some mistakes made in a previous version of this theory1 are corrected.