The purpose of this study was to analyze the relationship between the intra-cycle variation of the horizontal velocity of displacement of the center of mass (dV), the hand's and feet's velocity, as well as, to identify the variables that most predict the dV's, in butterfly stroke. The study was divided in two parts. The aim of Part I was to investigate the behavior of variables in study at slow swimming velocities and the purpose of Part II was the same but at high swimming velocities. 3 male Portuguese swimmers and 1 female swimmer, of international level were studied in Part I. The swimmers were submitted to an incremental set of 200 m butterfly swims. In the Part II, 7 Portuguese male swimmers of national and international level were studied. Each swimmer performed two maximal 25 m butterfly swims. Both protocols were recorded from four different plans, allowing a 3D analysis. It was calculated the dV, the 3D components (Vx, Vy, Vz) of the hand's velocity and the 2D components (Vx, Vy) of the feet's velocity. Several variables presented significant correlation coefficients with dV at all selected velocities (high velocity ranged from r = 0.58 for Vx-out to r = 0.82 for Vy-1dwn; slow velocity ranged from r = -0.45 for Vx-1dwn to r=0.73 for Vx-ups; overall velocity ranged from r= 0.34 for Vz-ent to r = 0.82 for Vx-ins). It was also computed a regression model to predict dV. For high velocity (up to 1.75 ± 0.09 m.s^-1), the variables that best predict dV were Vy during the first downbeat, Vx and Vy during the arm's insweep (r² = 0.93). At slow velocity (up to 1.48 m.s^-1), the variables included in the forward step-by-step regression model were Vx during upsweep, Vy and Vx during insweep (r² = 0.69). For overall velocity, the variables that most fit the regression model were Vx during upsweep, Vy during second downbeat and Vz during entry (r²= 0.94). In order to reduce dV, butterfliers should increase hand's velocity in all orthogonal components at the end of the underwater path, should increase the vertical velocity during the downbeats and decrease the velocity during the hand's entry.

• Segmental velocities are a determinant phenomenon for swimming performance and should be carefully analyzed by coaches and butterfliers.

• Butterfliers must finish the last phase of the underwater path with a high hand's velocity in order to reduce the speed fluctuation and increase the swimming velocity.

• Butterfliers should also pay more attention to downbeats, since they are important to reduce the speed fluctuation during the hand's entry, as well as, the arm's recovery.