A method based on energy balance is used to obtain the thresholds of parametric instabilities of the 'purely growing' and 'arithmetic mean' varieties which can exist in a plasma irradiated by two or more electromagnetic pump waves. These instabilities produce growing standing electron plasma waves at frequencies satisfying either &ohgr; =&ohgr;i, where &ohgr;i is the frequency of the ith pump wave, or &ohgr;= (&ohgr;i+&ohgr;j)/2, where i and j correspond to two different pump waves. Additionally growing ion standing waves of zero frequency or of frequency (&ohgr;i-&ohgr;j)/2 are produced. These coherent instabilities are found to be coupled in a sense with the usual 'decay' instability and, in the case of three or more pump waves, with each other. The results of this investigation are applied to a recent ionospheric heating experiment described in a companion paper.