A process is described for producing synthetic zeolites useful as catalysts with a MFI structure, a Si/Al atomic ratio from about 8 to 45 to 1 and very small primary crystallites. A Si source, an Al source and an organic template are reacted with one another under hydrothermal conditions. The process is carried out in the presence of seed crystals with an average particle size from roughly 10 to 100 nm, preferably from 20 to 50 nm, prepared from an earlier batch of synthetic zeolites with a MFI structure, without separation from the mother liquor. The process further includes conversion by ion exchange of the zeolites into an H form. Moldings may also be produced by the addition of binders and optionally catalytically active base metal and/or precious metal components before or after the moldings are produced. The zeolites as claimed in the invention are characterized by the combination of the following features: (a) Si/Al atomic ratio 8 to 45:1 (b) Size of the primary crystallites roughly 0.01 to 0.05 microns; (c) Ratio between longest and shortest axis of the primary crystallites: roughly 1.0 to 1.5:1; (d) Ratio between the intensity of the x-ray diffraction line with the highest intensity (D.sub.max=3.865.+-.0.015) and the intensity of the x-ray diffraction lines of ZSM 11-zeolite (D.sub.max=11.15 angstroms); mordenite (D.sub.max=9.06 angstroms); .alpha.-cristobalite (D.sub.max=3.345 angstroms); and analcim (D.sub.max=4.83 angstroms)>500:1.