In this paper we analyze multi-epoch Very Long Baseline Interferometry ( VLBI ) water maser observations carried out with the Very Long Baseline Array ( VLBA ) toward the high-mass star-forming region AFGL 2591 . We detected maser emission associated with the radio continuum sources VLA 2 and VLA 3 . In addition , a water maser cluster , VLA 3-N , was detected \sim 0.5 ^ { \prime \prime } north of VLA 3 . We concentrate the discussion of this paper on the spatio-kinematical distribution of the water masers towards VLA 3-N . The water maser emission toward the region VLA 3-N shows two bow shock-like structures , Northern and Southern , separated from each other by \sim 100 mas ( \sim 330 AU ) . The spatial distribution and kinematics of the water masers in this cluster have persisted over a time span of seven years . The Northern bow shock has a somewhat irregular morphology , while the Southern one has a remarkably smooth morphology . We measured the proper motions of 33 water maser features , which have an average proper motion velocity of \sim 1.3 mas yr ^ { -1 } ( \sim 20 km s ^ { -1 } ) . The morphology and the proper motions of this cluster of water masers show systematic expanding motions that could imply one or two different centers of star formation activity . We made a detailed model for the Southern structure , proposing two different kinematic models to explain the 3-dimensional spatio-kinematical distribution of the water masers : ( 1 ) a static central source driving the two bow-shock structures ; ( 2 ) two independent driving sources , one of them exciting the Northern bow-shock structure , and the other one , a young runaway star moving in the local molecular medium exciting and molding the remarkably smoother Southern bow-shock structure . Future observations will be necessary to discriminate between the two scenarios , in particular by identifying the still unseen driving source ( s ) .