We investigate experimentally the nonlocal phase modulation of multiple-frequency-mode, continuous-variable entangled twin beams. We use a pair of electro-optical phase modulators to modulate the entangled probe and conjugate light beams produced by four-wave mixing in hot rubidium vapor. A single phase modulator in either one of the twin beams reduces the two-mode squeezing signal. The overall quantum entanglement is preserved, however, as the modulator nonlocally distributes the beam correlations among frequency modes of the multimode fields. The two-mode squeezing can be recovered by reversing the mixing with an additional out-of-phase electro-optical phase modulator (EOM) in the other beam.