The oil produced from sunflower seed is primarily used for human consumption. It can substitute for other edible vegetable oils, such as rapeseed oil, processed into biodiesel in the EU. This paper assesses the influence of crude oil futures on new crop sunflower seed futures in Hungary during the growing seasons of sunflower by applying standard cointegration analysis for the period 2004-2013. Tests were performed for the entire period and each sunflower growing season. For comparison, the influence of Paris rapeseed futures on sunflower seed futures was also assessed. The contrasting estimations for the global and seasonal characteristics of the variables suggest that standard cointegration analysis may not be appropriate for multiannual price series of agricultural commodities with strong seasonality in production because it will not capture the periodical shocks in supply and demand. The results are briefly discussed from the aspect of the fundamentals of the sunflower seed market.