Well preserved examples of Milankovitch-driven cyclicity in the Triassic sedimentary record include Triassic-Jurassic lake sedimentary cycles, marine cyclic carbonates on small Middle Triassic platforms in the Dolomite Alps, and off-shelf facies equivalent to Late Triassic large passive-margin platforms. In contrast, the Late Triassic Hungarian shallow marine carbonate platform that formed on the Southern margin of Tethys records a far from perfect Milankovitch eustatic signal. These carbonate cycles contain subtidal skeletal wackestone/packstone, tidal laminites, and paleosols. The cycles include not only transgressive laminites (the classic Lofer cycles): some cycles contain regressive laminites, whereas other cycles have both transgressive and regressive laminites. The stratigraphic successions do not show the clear bundling of five precessional cycles into larger-eccentricity cycles. The poor record of Milankovitch sea-level changes is interpreted to be due to many missed beats in the platform stratigraphy. Missed beats are evidenced by (1) caliches and paleosols and (2) thick amalgamated subtidal carbonates, and may result from precessional sea-level fluctuations either not flooding the platform or flooding it too deeply to allow shallowing up to sea level in one precessional beat. Fourth-order bundling of the cycles is weak, with fewer than the typical 5 cycles/100 k.y. bundle and far less than 20 cycles for inferred 400 k.y. eccentricity bundles. Fischer plots of the Hungarian cycles show third-order bundling that matches Aigner's (1992) sea-level curve from the German Muschelkalk basin but is less similar to the Haq et al. (1987) global sea-level curve.