The interactions between two poly(allylamine)/poly(styrene sulfonate) multilayers made of 4.5 and 5 bilayers are investigated by the surface force apparatus (SFA). As the two surfaces approach, one reaches a threshold point where a repulsion sets in, until they become barely compressible. Repetitive load/unload cycles show that, once compressed, the films remain almost in their compressed state. This indicates that the poly(allylamine)/poly(styrene sulfonate) films are in a glassy state, in marked difference with the SFA findings on poly-(L-lysine)/poly-L-glutamic acid) multilayers. These results are discussed in the light of linearly and exponentially growing films.