A method for the production of one or more olefins comprising the steps of: (i) gasification reaction of lignocellulosic materials and/or other organic components contained in residue of a renewable natural agricultural raw material, resulting in the production of a mixture of carbon monoxide and hydrogen (synthesis gas); (ii) formation of methanol from the synthesis gas generated in step (i); and (iii) transformation of the methanol obtained in step (ii), directly or indirectly from the intermediate dimethyl ether, into one or more olefins, characterized in that the method is integrated with a method of processing the renewable natural agricultural raw material, so that the residue generated in the method of processing the renewable natural agricultural raw material is directed to the gasification reaction of step (i), wherein the method of processing the renewable natural agricultural material comprises the fermentation of the sugar or the starch, provided that the latter is previously hydrolyzed, found in the renewable natural agricultural raw material, resulting in the production of ethanol and carbon dioxide, and wherein the method for the production of one or more olefins further comprises at least one of the following alternatives: (a) the carbon dioxide generated in the method of processing the renewable natural agricultural raw material is reduced to carbon monoxide by means of a reaction with hydrogen or with organic materials containing carbon, oxygen and hydrogen, generating a complementary amount of synthesis gas, which is directed to step (ii) of methanol formation; (b) the water generated as a by-product in step (iii) is reused in at least one step of the method of processing the raw material; and (c) the streams leaving the gasification reactor and those leaving the step of formation of olefins from methanol provide the necessary heat to reduce the residual humidity of the residue of the renewable natural raw material to the levels required for the gasification reaction, or to preheat the charge in the gasification reactor, the charge of methanol and/or dimethyl ether fed into the dehydration reactor, wherein preferably the one or more olefins comprise(s) propylene, and optionally, ethylene and butylene. (a) the carbon dioxide generated in the method of processing the renewable natural agricultural raw material is reduced to carbon monoxide by means of a reaction with hydrogen or with organic materials containing carbon, oxygen and hydrogen, generating a complementary amount of synthesis gas, which is directed to step (ii) of methanol formation; (b) the water generated as a by-product in step (iii) is reused in at least one step of the method of processing the raw material; and (c) the streams leaving the gasification reactor and those leaving the step of formation of olefins from methanol provide the necessary heat to reduce the residual humidity of the residue of the renewable natural raw material to the levels required for the gasification reaction, or to preheat the charge in the gasification reactor, the charge of methanol and/or dimethyl ether fed into the dehydration reactor, wherein preferably the one or more olefins comprise(s) propylene, and optionally, ethylene and butylene.