Abstract: When a spherical particle moves in an incompressible laminar steady three-dimensional closed flow it may be attracted to periodic orbits. Such periodic orbits arise due to the forces acting on the particle during its motion. Attractors due to inertia forces acting in the bulk of the fluid are well known and may lead to Lagrangian Coherent Structures (LCS) of particles. In this presentation other types of attractors are presented, which are not caused by inertia, but by forces acting on the particle of finite size when it moves near a boundary of a closed or spatially periodic flow. The resulting attractors, called Finite Size Coherent Structures (FSCS), mainly depend on the three-dimensional streamline topology and on the particle size. To distinguish between LCS and FSCS, inertia effects are minimized by considering nearly density-matched finite-size particles. It turns out that FSCS can form very rapidly. Examples of FSCS are discussed presenting numerical and experimental results.