One aspect of activity engagement that has received only limited attention is that related to the modeling of interactions among household members. Within a household, members allocate tasks among each other, make trade-offs with respect to activity time allocation, and pursue activities jointly. These household interactions are extremely critical in a person's activity-travel decision-making process. This paper develops a structural equations model system of activity task and time allocation among household members in multi-person households. The structural equation model system considers the relationships among the frequencies and durations of different activity types across household members. The model system is capable of capturing the task allocation, activity trade-off, and activity complementarity that exists in households.