We use the method of multiple scales (MMS) to study small perturbations governed by a parameter ε of a harmonic oscillator by a small term with a large delay. These systems differ significantly from others where small terms have script O sign(1) delays; or an script O sign(1) term has script O sign(1) delay in a system near a Hopf bifurcation. Here the slow flow in time ε t depends strongly on ε even at lowest order and itself has an script O sign(1) delay. The MMS has already been applied elsewhere for such systems but only to first order and with attention restricted to periodic and quasiperiodic solutions. Here we address transients as well as proceed to second order. The second order analysis holds unless a special resonance occurs (we assume it does not). Several numerical examples are presented. In each case the slow flows are infinite-dimensional show strong ε-dependence require significantly less computation time than the full solutions yet agree well with the same. © 2005 Springer Science + Business Media Inc.