A structural multivariate long memory model of the US gasoline market is employed to disentangle structural shocks and to estimate the own-price elasticity of gasoline demand. Our main empirical findings are: 1) there is strong evidence of nonstationarity and mean-reversion in the real price of gasoline and in gasoline consumption; 2) accounting for the degree of persistence present in the data is essential to assess the responses of these two variables to structural shocks; 3) the contributions of the different supply and demand shocks to fluctuations in the gasoline market vary across frequency ranges; and 4) long memory makes available an interesting range of convergent possibilities for gasoline demand elasticities. Our estimates suggest that after a change in prices, consumers undertake a few measures to reduce consumption in the short- and medium-run but are reluctant to implement major changes in their consumption habits. Keywords: fractional integration, gasoline demand, price elasticity, structural model Classification: Q41, Q43, C32