Conditions are described under which vesicles formed by caprylic acid and oleic acid in water are able to undergo autopoietic self-reproduction-namely an increase of their population number due to a reaction which takes place within the spherical boundary of tile vesicles themselves. This is achieved by letting a certain amount of the neat water-insoluble caprylic or oleic anhydride hydrolyze at alkaline pH : the initial increase of the concentration of the released acid/carboxylate is extremely slow (several days to reach the conditions for spontaneous vesicle formation), but afterwards, the presence of vesicles brings about a rapid second phase leading to more and more vesicles being formed in an overall autocatalytic process. The catalytic power of the caprylic acid and oleic acid vesicles toward the hydrolysis of the corresponding anhydride is documented in a set of independent experiments. In these experiments, the hydrolysis was carried out in the presence of vesicles at a pH corresponding approximately to the pK of the acid in the vesicles. The process of autopoietic self-reproduction of caprylic acid and oleic acid vesicles is studied as a function of temperature : by increasing temperature (up to 70 degrees C), the exponential time progress of vesicle formation tends to become steeper while the long initial slow phase is significantly shortened. The caprylic acid and oleic acid vesicles are characterized by electron microscopy and by determining their internal volume. The question whether and to what extent these vesicles form a classic chemical equilibrium system-in which namely the free surfactant is in equilibrium with the aggregates-is also investigated.