The data for the mean squared transverse momentum p 2 t (E t ) as function of transverse energy E t of J/ψ and ψ ′ produced in Pb-Pb collisions at the CERN-SPS are analyzed and it is claimed that they contain information about the time structure of anomalous suppression. A transport equation which describes transverse motion of J/ψ and ψ ′ in the absorptive medium is proposed and solved for a QGP and a comover scenario of suppression. While the comover approach accounts for the data fairly well without adjusting any parameter, the fit to the data within the QGP scenario requires to assume anomalous suppression to become effective rather late, 3−4 fm/c after the nuclear overlap.The discovery in 1996 of anomalous J/ψ suppression in Pb-Pb collisions at the SPS has been one of the highlights of the research with ultrarelativistic heavy ions at CERN [1]. Does it point to the discovery of the predicted quark gluon plasma (QGP)? Six years later the situation is still confused, since several models -with and without the assumption of a QGP -describe the observed suppression, after at least one parameter is adjusted. The data on the mean squared transverse momentum p 2 t (E t ) [2] for the ψ (this symbol stands for J/ψ and ψ ′ ) in the regime of anomalous suppression and as a function of transverse energy E t have received less attention -for no good reason. We claim: p 2 t (E t ) contains additional information about the nature of anomalous suppression and may help to distinguish between different scenarios. In this paper we investigate how the time structure of anomalous suppression influences the values p 2 t (E t ). This idea has already been considered more than 10 years ago [3] (c.f. also more recent works [4,5]) and is based on the following observation ( Fig.1): Anomalous suppression is not an instantaneous process, but takes a certain time depending on the mechanism. During this time ψ's produced with high transverse momenta may leak out of the parton/hadron plasma and escape suppression. As a consequence, low p t ψ's are absorbed preferentially and the p 2 t of the surviving (observed) ψ's show an increase δ p 2 t , which grows monotonically with the mean time t A , when anomalous absorption acts [5]. In this letter we propose a general formalism of how to incorporate the effect of leakage into the various models, which have been proposed to describe 1