A process for cracking an olefin-containing hydrocarbon feedstock which is selective towards light olefins in the effluent, the process comprising passing a hydrocarbon feedstock containing one or more olefins through a moving bed reactor containing a crystalline silicate catalyst selected from an MFI-type crystalline silicate having a silicon/aluminium atomic ratio of at least 180 and an MEL-type crystalline silicate having a silicon/aluminium atomic ration of from 150 to 800 which has been subjected to a steaming step, at an inlet temperature of from 500 to 600° C., at an olefin partial pressure of from 0.1 to 2 bars and the feedstock being passed over the catalyst at an LHSV of from 5 to 30 h−1 to produce an effluent with an olefin content of lower molecular weight than that of the feedstock, intermittently removing a first fraction of the catalyst from the moving bed reactor, regenerating the first fraction of the catalyst in a regenerator and intermittently feeding into the moving bed reactor a second fraction of the catalyst which has been regenerated in the regenerator, the catalyst regeneration rate being controlled whereby the propylene purity is maintained constant at a value corresponding to the average value observed in a fixed bed reactor using the same feedstock, catalyst and cracking conditions, for example at least 94 wt %.