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A discrete-continuous choice model of time allocation to two types of discretionary activities is formulated based on the concept of random utility maximization. The model development takes into account the discreteness inherent in daily activity engagement and time allocation (ie one type of activity may not be engaged, therefore no time may be allocated to it at all, during a day). Without requiring simplifying assumptions other than the one that at least one of the two types of activities will be engaged, the utility model is formulated as a doubly-censored Tobit model. This theoretical framework is applied to study daily time allocation to in-home and out-of-home discretionary activities while using, as explanatory variables, work schedules and commute characteristics as well as residential, household and personal attributes. A weekly time-use data set from the Netherlands is used in the statistical analysis. To account for heterogeneity in the data set comprising repeated measurements of daily time use for each respondent, an error component is introduced into the doubly-censored Tobit models. A non-parametric approach is adopted for model estimation using mass points. Behavioral implications of model estimation results are discussed. The validity of a procedure to correct estimated t-statistics proposed for repeated measurement data is also discussed.(A) For the covering abstract see IRRD 886400.