Positron annihilation lifetime measurements were carried out under different evacuation temperatures for zeolite NaY, HY and NH_4Y. Four lifetime components have been observed in these systems. The two shorter ones, τ_1 and τ_2, were assigned to positron annihilation in the bulk, self-annihilation of ρ-Ps, pick-off annihilation of ο-Ps in the bulk and annihilation of positron trapped in the cages. The two longer ones, τ_3 and τ_4, were assigned to annihilation of ο-Ps on the surface and in the cages of the zeolites respectively. The Brönsted acid in the zeolites oxidized o-Ps readily, so that the o-Ps lifetime τ_3 and τ_4 were reduced significantly in zeolite HY. The deammoniation of NH_4Y at higher evacuation temperatures can be monitored through measurements of o-Ps lifetimes. Brönsted acid in the zeolites does not inhibit the formation of o-Ps. However, o-Ps annihilates more readily on the surface as the concentration of Brönsted acid is increased, and hence the value of I_3 much largerthan I_4 in HY. The o-Ps annililation rates on the surface and in the cages, λ_3 and λ_4, are linearly proportional to the concentration of of Brönsted acid in the zeolites. First-order kinetics has been applied to the oxidation reactions of o-Ps and apparent rate constants k_3 and k_4, are 9.67×10~7 (mmol/g)s~(-1) and 2.36×10~7 (mmol/g)~(-1) s~(-1) respectively. The experimental results obtained demonstrate that positron annihilation spectroscopy is a sensitive technique to probe thesurface properties and pore structure of porous materials