In the direct product of the phase and parameter spaces, we define the \emph{perturbing region}, where the Hamiltonian of the planar three-body problem is \(\Cd^k\)-close to the dynamically degenerate Hamiltonian of two uncoupled two-body problems. In this region, the \emph{secular systems} are the normal forms that one gets by trying to eliminate the mean anomalies from the perturbing function. They are P{ö}schel-integrable on a transversally Cantor set. This construction is the starting point for proving the existence of and describing several new families of periodic or quasiperiodic orbits: short periodic orbits associated to some secular singularities, which generalize Poincar{é}'s periodic orbits of the second kind (''Les M{é}thodes nouvelles de la m{é}canique c{é}leste'', first Vol., Gauthiers-Villars, Paris, 1892--1899); quasiperiodic motions with three (resp. two) frequencies in a rotating frame of reference, which generalize Arnold's solutions (\textit{Russian Math. Survey}~\textbf{18} (1963), 85--191) (resp. Lieberman's solutions; \textit{Celestial Mech.}~\textbf{3} (1971), 408--426); and three-frequency quasiperiodic motions along which the two inner bodies get arbitrarily close to one another an infinite number of times, generalizing the Chenciner-Llibre's invariant ''punctured tori'' (\textit{Ergodic Theory Dynamical Systems}~\textbf{8} (1988), 63--72). The proof relies on a sophisticated version of {\scshape kam} theorem, which itself is proved using a normal form theorem of M. Herman (''D{é}monstration d'un Th{é}or{é}me de V.I.~Arnold,'' S{é}minaire de Syst{é}mes Dynamiques and Manuscipts, 1998)