In today’s emerging information systems, it is natural to have data distributed across multiple sites. We define a System of Databases (SyDb) as a collection of autonomous and heterogeneous databases. R-SyDb (System of Relational Databases) is a restricted form of SyDb, referring to a collection of relational databases, which are independent. Similarly, X-SyDb (System of XML Databases) refers to a collection of XML databases. Global integrity constraints ensure integrity and consistency of data spanning multiple databases. In this dissertation, we present (i) Constraint Checker, a general framework of a mobile agent based approach for checking global constraints on R-SyDb, and (ii) XConstraint Checker, a general framework for checking global XML constraints on X-SyDb. Furthermore, we formalize multiple efficient algorithms for varying semantic integrity constraints involving both arithmetic and aggregate predicates. The algorithms take as input an update statement, list of all global semantic integrity constraints with arithmetic predicates or aggregate predicates and outputs sub-constraints to be executed on remote sites. The algorithms are efficient since (i) constraint check is carried out at compile time, i.e. before executing update statement; hence we save time and resources by avoiding rollbacks, and (ii) the implementation exploits parallelism. We have also implemented a prototype of systems and algorithms for both R-SyDb and X-SyDb. We also present performance evaluations of the system.