As offshore industry progressively moves towards deeper water, coupled dynamic analysis of such structures with mooring lines and risers becomes increasingly important because of the growing influence of mooring lines on the response of these structures. Experimental studies for such deepwater structures with mooring lines face serious problems due to the involved scaling and modeling issues. For such studies therefore a numerical tool capable of simulating the coupled dynamics of offshore structures is almost indispensable where the effect of mooring lines, loads arising from structural elements such as heave damping plates which are primarily due to fluid viscosity, external effects such as wind loads in case of floating wind turbines etc. are all coupled with the wave loads acting on the structure. It is widely acknowledged that for such a general and versatile numerical tool a time domain solution scheme is preferred over frequency domain solutions, particularly if nonlinearities in wave loads, mooring lines etc. are to be considered albeit in some simplified way. Based on such a premise, a solution scheme following a 3D numerical wave tank approach but with significant difference and novelty in its implementation have been under development. The developed method is capable of simulating long duration wave-structure interactions including important nonlinearities in wave loads, and in principle can also consider effects from many external sources such as linear and nonlinear mooring stiffness. While many aspects of the scheme including a validation and verification process is reported elsewhere, the purpose of the present paper is to study in detail the effect of linear and nonlinear mooring line stiffness on practical offshore configurations. As regards wave induced hydrodynamic loads, both linear loads as well as nonlinear loads arising from steep nonlinear incident wavers are considered. Results demonstrate that nonlinear mooring stiffness can have significant influence on the response of the structure. The influence of nonlinearities in mooring stiffness is relatively more pronounced when water depth is less while in deeper water a linear stiffness appears to be adequate in capturing the structure's response. The influence of hydrodynamic nonlinearity is however significant in all cases. These and other important results for practical offshore structures with different mooring configurations are presented and discussed in the paper.