The large-scale dynamics of the ocean include motions that vary on a wide range of time scales. In numerical models of ocean circulation, it is widespread practice to split the fast and slow motions into separate subproblems that are solved by different techniques. These matters will be discussed in two talks in consecutive weeks. The present talk will give an overview of time scales and time splitting and will describe some problems that can arise with multiple time scales and conservation of mass in layered ocean circulation models. Part 2 will describe some issues related to conservation of momentum and will show the results of numerical computations that test two different ways to formulate the momentum equation in the context of a time splitting.