We exhibit the solution of the initial-value problem for the system of 2N + 2 oscillators characterized by the Hamiltonianwhere N is an arbitrary positive integer, Ω, b and ω 2 n are N + 2 arbitrary real constants, qm, qm with m = 0, 1, . . ., N are the 2N + 2 canonical coordinates and pm, pm the corresponding 2N + 2 canonical momenta.In the classical context the solution is completely periodic with period T = 2π/|Ω| (for arbitrary initial data).In the quantal context the (infinitely degenerate) spectrum is equispaced, with spacing |Ω|; all the corresponding eigenfunctions are also exhibited.This finding obtains as special case of a more general (new) class of isochronous Hamiltonians.