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We develop a mathematical description of the response of weakly nonlinear systems to second-order memory mechanisms. Our description is based on a time-varying gain-modulation function. We show that intermodulation (IM) products arising from interactions at baseband have phase symmetries different from both interactions at second harmonic frequencies and gain compression and, thus, may be readily distinguished through measurement. We also demonstrate a technique for measuring and aligning the phase of IM products outside the measurement bandwidth of our instrumentation to identify contributions to memory with broad frequency response.