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Anomalous fluctuations in magnetoconductance are observed above the melting temperature T m of two-dimensional electrons on liquid 4 He. In the 2D solid the low frequency Corbino magnetoconductivity s͑B͒ is increased by coherent Bragg-Cerenkov coupling to ripplons on the helium surface. Above T m (plasma parameter G 127), fluctuations in s͑B͒ suggest a microstructure with significant ordered and coupled regions. The fluctuations decrease continuously with temperature up to T f ͑2.8 6 0.3͒T m at G 46 6 5. Fluctuations also occur in the 2D electron solid at high drive amplitudes.[S0031-9007(97)05054-0]