  We prove a bubble tree convergence theorem for a sequence of closed
Hamiltonian Stationary Lagrangian surfaces with bounded areas and Willmore
energies in a complete K{\"a}hler surface. We also prove two strong compactness
theorems on the space of Hamiltonian stationary Lagrangian tori in $\mathbb
C^2$ and $\mathbb{CP}^2$ respectively.
