We demonstrate, theoretically and experimentally, that the irradiation of a powder sample containing spin-1 nuclei by two of the three characteristic nuclear quadrupole resonance (NQR) frequencies can result in several echo signals at the third NQR frequency. One of these echoes, the principal echo, has the same shape and time of occurrence as an echo produced after a pair of single-frequency excitations. The other echoes are not equivalent to any single-frequency echo. These secondary echoes are the focus of this paper. The time of occurrence and shape of the secondary echoes are determined by the correlation of the distribution in one transition frequency to the distribution in a second transition frequency. This correlation is in turn determined by the correlation between the distributions of the electric field gradient components, which is itself determined by the types and concentrations of crystalline defects present. We present the optimal conditions to observe such secondary echoes and compare theory with experiment using N-14 (I=1) in powder samples of sodium nitrite and RDX. (C) 2003 American Institute of Physics.