  Strong numerical evidence is presented for the existence of a continuous
family of time-periodic solutions with ``weak'' spatial localization of the
spherically symmetric non-linear Klein-Gordon equation in 3+1 dimensions. These
solutions are ``weakly'' localized in space in that they have slowly decaying
oscillatory tails and can be interpreted as localized standing waves
(quasi-breathers). By a detailed analysis of long-lived metastable states
(oscillons) formed during the time evolution it is demonstrated that the
oscillon states can be quantitatively described by the weakly localized
quasi-breathers.It is found that the quasi-breathers and their oscillon
counterparts exist for a whole continuum of frequencies.
