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The problem of consistent estimation of the unknown parameters of linear time-invariant continuous-time systems is considered. The unknown parameter set is assumed to be compact, and only noisy observations of the system output are available. Sufficient conditions are derived for global strong consistency of the maximum-likelihood parameter estimates. The consistency proof exploits a recent result due to Delchamps concerning smoothness of the algebraic Riccati equation in the system parameters. This smoothness result has been tacitly assumed in the literature on local consistency of the parameter estimates. The previous global consistency results have been obtained under the restrictive assumption of finite parameter sets.