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An analysis of electromagnetic-wave propagation in dense plasmas when the wave frequency is below the cutoff frequency is presented. Under such conditions, the wave amplitude is usually exponentially attenuated due to collisionless skin effect. It is shown that combining multiple plasma layers of various densities induces a surface-wave resonance, which greatly enhances electromagnetic-wave transmission. Absolute transmission can be achieved even for plasma thickness of many skin depths. Resonant conditions are investigated analytically and numerically.