The equations of motion of the Buckingham system are the ones of a two-body problem defined by the Hamiltonian H=12(px2+py2)+Ae−Bx2+y2−M(x2+y2)3, $$ H= \frac{1}{2} \bigl(p_{x}^{2}+p_{y}^{2} \bigr) + A e^{-B \sqrt{x ^{2}+y^{2}}}-\frac{M}{ (x^{2}+y^{2} )^{3}}, $$ where A $A$, B and M are positive constants. The angular momentum pθ:=xpy−ypx $p_{\theta }:= x p_{y}- y p_{x}$ and this Hamiltonian are two independent first integrals in involution. We denote by Ih (respectively, Ic $I_{c}$) the set of points of the phase space where H (respectively, pθ $p_{\theta }$) takes the value h (respectively, c $c$). Due to the fact that H and pθ are first integrals, the sets Ih and Ihc=Ih∩Ic are invariant under the flow of the Buckingham systems. We describe the global dynamics of the Buckingham system describing the foliation of its phase space by the invariant sets Ih $I_{h}$, the foliation of the invariant set Ih by its invariant subsets Ihc $I_{hc}$, and the foliation of invariant set Ihc by the orbits of the system.