We propose a stochastic model  to explain   the  long time scale  
dynamics  of Cytotoxic Antigen- experienced (AE) (memory) T Cell Clones.
The clonal expansion   is the result of a  complex dynamical process in  
which the main actors are the  acute and chronic antigenic  stimuli,  
and the local environment created by the Cytokinic network in 
peripheral tissues. To describe the homeostasis, we introduce 
a size-landscape with several minima  corresponding to the local 
quasi-equilibrium states of the clonal size.   
These states are reached under: i. the impulse of external acute 
stimuli  which cause  rapid jumps; ii. the chronic stress causing 
a slow diffusion; iii.  physiological regulatory mechanisms. 
The chronic stress  has a  relevant role on long time  
scale dynamics via   cross-reactivity   and induced cytokinic 
activity during heterologous pathogen infection.