This paper studies the comovements between the daily returns of forwards on natural gas traded in the NYMEX with maturities of one, two and three months. We identify a structural multivariate BEKK model using a recursive assumption, whereby shocks to the volatility of the returns are transmitted from the short to the long section of the forward curve. We find strong evidence of spillover effects in the conditional first moments, for which we show that the transmission mechanism operates from the shorter to the longer maturity. In terms of reduced-form conditional second moments, the shorter the maturity, the higher the volatility of the return is, and the more the returns become independent from the other returns and follow the dynamics of the underlying commodity price. The evidence from the structural second moments indicates that the longer the maturity is, the higher the uncertainty about the returns is. We also show that the higher the structural variance of a returrelative to that of another return, the stronger the correlation is betweenthe two.