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The transmission of confidential information over LMDS networks is investigated in the present paper from an information-theoretic standpoint. The major factor impairing the link performance at these networks is rain attenuation, a physical phenomenon exhibiting both spatial and temporal variation. Based on an accurate channel modeling, analytical expressions of the probability of non-zero secrecy capacity and the outage probability for this type of networks are provided, giving for the first time an information-theoretic approach of the problem of secure transmission for LMDS networks. Useful conclusions are drawn through extended numerical results suggesting the increase of operational frequency and the use of more directional antennas to improve security in transmission of confidential messages for this type of networks.