In this chapter, we delve into two generalized models of the equilibrium problem: the variational inclusion problem and variational relation problems. In fact, under appropriate conditions, these problems are equivalent. However, with applications in mind, we present results about properties of the solutions to these problems independently. Similar to previous chapters, we will explore the existence of solutions and the stability of these problems. First we prove several existence results for the variational relation problem. Then, applying these results, we obtain some existence conditions for the variational inclusion problems. We employ semicontinuity properties of set-valued maps to establish sufficient conditions for the (semi)continuity of solution maps and prove well-posedness conditions for the considered variational inclusion problem. As for the variational relation problem, we also provide stability results related to (semi)continuity, convergence, and Holder calmness of solution maps. The results presented in this chapter encompass all the findings for these models, and we acknowledge that there remain many topics worthy of further study.