Isothermal cis-trans isomerization of polyacetylene (PA) films proceeds according to a stretched-exponential function of time with an exponent alpha (0 < alpha < 1). A mechanism is proposed for the cis-trans isomerization. Cis-trans isomerization of PA occurs under the condition that the molecular axis is almost fixed. The interspace-diffusion model is effective in simply describing the intermolecular cooperative motions of neighboring chains to avoid the intermolecular constraints for cis-trans isomerization motion. If an interspace appears in the neighborhood of a cis bond (or moving unit of cis state), this cis unit is assumed to change to the trans state instantaneously. Using the continuous-time random walk model, the decay of survival probability of a cis unit can be expressed by the stretched-exponential function under the assumption of the distribution of activation energy for cis-trans isomerization. The relationship between the two-state model and the interspace-diffusion model is discussed.