Time-dependent properties of coherent range-resolved backscatter from a sea surface with simple floating targets are studied using two-dimensional (2-D) direct numerical simulations based on a first-principles boundary integral equation technique. The deterministic sea surface is generated according to a wind-driven wave spectrum. Target motion is modeled in a simplified way as that of a massless object heaved by orbital currents. Calculations can be performed at a broad range of grazing angles and at both HH and VV polarizations. The paper gives examples of range-time records of the X-band backscatter and then focuses on the Doppler characteristics of the simulated echoes. Differences between the responses of floating targets and sea surface are rather conspicuous, and appear to be caused primarily by dissimilarities in cross-section modulation behavior.