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We consider varying coefficient Cox models with high-dimensional covariates.We apply the group Lasso method to these models and propose a variableselection procedure. Our procedure copes with variable selection and structureidentification from a high dimensional varying coefficient model to asemivarying coefficient model simultaneously. We derive an oracle inequalityand closely examine restrictive eigenvalue conditions, too. In this paper, wegive the details for Cox models with time-varying coefficients. The theoreticalresults on variable selection can be easily extended to some other importantmodels and we briefly mention those models since those models can be treated inthe same way. The models considered in this paper are the most popular modelsamong structured nonparametric regression models. The results of a smallnumerical study are also given.

Variable selection and structure identification for varying coefficient Cox models