A time-varying coefficient demand system, the Markov switching almost ideal demand model, is proposed to shed new light on change over time in the structure of French meat and fish demand. The main feature of this model is that the switching mechanism from one structure of demand to the other is controlled by an unobserved variable that follows a Markov chain. Our model accurately captures the two Bovine Spongiform Encephalopathy (BSE) crises of recent years. We estimate that the 1996 BSE crisis lasted almost three years, whereas the second BSE crisis for just lasted five 4-week periods.