During the initial experimental phase, LHD, a stellarator of the heliotron/torsatron variety presently under construction, will operate at a magnetic field lower than the nominal one. In this scenario, the frequency of the available gyrotrons (chosen in view of second harmonic heating at full field operation) will be resonant with the third or the fourth harmonic of the electron gyrofrequency. The aim of this article is to analyse the electron cyclotron resonance heating (ECRH) at these high harmonics. By using linear absorption theory, together with transport predictions, good absorption is found over a wide density range for third harmonic heating. In the case of the fourth harmonic, the conditions for absorption are considerably more critical, but non-negligible heating (single pass absorption ≳ 10%) is expected in very low density, high temperature target plasmas. Owing to the strong temperature dependence of the absorption mechanism, heating at higher harmonics presents some peculiar characteristics. Quasi-linear effects are found to improve the absorption properties (as compared with those of linear theory), and bifurcation phenomena, as well as a critical power threshold, might appear. The physical origin and the consequences of these effects are discussed.