Abstract: Vibrating-reed measurements in La1.8Sr0.2CuO4 in a magnetic field show that the flux-line structure (FLS) becomes uncoupled from the material at a temperature TH of 23 K, much below the critical temperature of the sample, which is 32 K. The behavior is similar to that found in Bi2Sr2CaCu2O8 but shows some significant differences, the most important being that TH changes little with magnetic field throughout the measured field range (0.01 TH1 T). For low fields, TH is below the reversibility line of the magnetization. This seems to imply that the reversibility line and the line at which the FLS softens have to be considered as distinct physical phenomena. It is argued that neither flux-lattice melting nor giant flux creep considered separately can account for the data in a wholly satisfactory manner.