In the framework of an international collaboration, the critical decay constant (α0 = β/Λ), and delayed neutron fraction (β) of the CROCUS reactor were measured by teams of EPFL/PSI, CEA and SCK•CEN research institutes using the Rossi-α and Power Spectral Density neutron noise measurement techniques. These measurements contribute to the experimental database of kinetic parameters used to improve nuclear data files and validate modern methods in Monte Carlo codes. CROCUS is a light-water zero-power reactor composed of two interlocked fuel zones with square lattices of different pitches, and different enrichments. An extensive experimental campaign was carried out at various critical levels and in four different subcritical configurations, with numerous detectors setups. This article is focusing on the first results in critical state for two powers (40 mW and 200 mW) with the most sensitive detectors, namely 1 g 235U fission chambers set at the core-reflector interface. Values of α0 and β determined by the three institutes and with the different techniques are consistent for the configurations envisaged. Results for α0 are in agreement within one standard deviation with MCNPv5-1.6 calculation results, whereas discrepancies are observed for β, up to 10% depending on the used nuclear data library.