The invention relates in particular to a greenhouse of the "Venlo" type, comprising a framework (1-3) for supporting at least a roof structure. Said roof structure is provided with at least one, preferably asymmetric, roof section comprising a substantially south-facing south deck (5) and, adjoining said south deck, a north deck (6). The north deck and south deck are bounded by a gutter (7) on one side and by a higher-positioned ridge (8) on the opposite side. The north deck is provided with panes and air windows (19) and the south deck is provided with at least two, preferably linear, Fresnel lenses (10, 11) disposed between the gutter and the ridge, each Fresnel lens having associated absorption elements (12, 13) provided therebelow, which Fresnel lenses are arranged for tracking, with at least two degrees of freedom, the position of the sun by means of a moving mechanism (14) connected to the absorption elements. The invention provides, inter alia, a special moving mechanism, whilst also the constructions of the Fresnel lenses, the absorption elements and the panes are innovative.