Auroral kilometric radiation has been attributed to an electron cyclotron maser instability and is known to have components at both the cyclotron frequency and its harmonics. Solar microwave spike bursts and similar bursts from flare stars are also thought to be maser emission at harmonics of the cyclotron frequency. Fundamental X mode growth is known to dominant when &ohgr;P/&OHgr;e≲0.3. At higher &ohgr;P/&OHgr;e the dominant radiation from the maser depends on the prevailing plasma conditions. In particular, it is shown that the dominant radiation can be (1) fundamental Z or O mode or second-harmonic X mode radiation when 0.3≲&ohgr;P/&OHgr;e≲1, (2) fundamental Z mode or second-harmonic X mode radiation when 1≲&ohgr;p/&OHgr;e≲√2, (3) second -harmonic O mode or third harmonic X mode radiation when √2,≲&ohgr;P/&OHgr;e≲√3, or (4) second-harmonic Z mode radiation when √3≲&ohgr;p/&OHgr;e≲√6. In these ranges of &ohgr;p/&OHgr;e, X mode growth at the relevant harmonic tends to be suppressed if the distribution of the energetic electrons only has a loss cone anisotropy, whereas it tends to dominant if the distribution is peaked at large pitch angles.