Direct time integration is a widely-used method for the analysis of loads and motions of mooring and floating systems. Nonlinear and transient effects can be easily accounted for in time domain analyses but it is a computationally expensive method, especially for explicit solvers which are limited by the timestep size to meet numerical stability requirements. There is potential in using multirate time to reduce computation times. This paper presents the development and evaluation of a multirate timestepping algorithm based on the Modified Euler integration method for the solution of mooring dynamics. The temporal synchronization as well as spatial boundary conditions needed for coupling the partitioned line segments with different spatial discretizations are presented. The stability parameters and gains in computational efficiency of the method are evaluated with numerical experiments based on a simple test case.