Process for the production of a subcooled liquefied natural gas stream from a natural gas feed stream, of the type comprising the following steps: - precooling the natural gas feed stream by passing it through a first heat exchanger in order to obtain a feed stream precooled to a temperature below -20°C; - liquefying the precooled feed stream by passing it through a second heat exchanger in order to obtain at least one liquefied natural gas stream at a temperature below -80°C; - subcooling the liquefied natural gas stream by passing it through a third heat exchanger in order to obtain a liquefied natural gas stream subcooled to a temperature below -120°C; - placing the feed stream in a heat exchange relationship in the first heat exchanger with a first stream of refrigerant; - placing the precooled feed stream in a heat exchange relationship in the second heat exchanger with a second stream of gaseous refrigerant circulating in a second refrigeration cycle, the second gaseous refrigerant stream being produced from a second gaseous stream of expanded fluid coming from a second dynamic expansion turbine; - placing the liquefied natural gas stream in a heat exchange relationship in the third heat exchanger with a third refrigerant stream circulating in a third refrigeration cycle, the third refrigerant stream being produced at least partly from a third gaseous stream of expanded fluid issuing from a third dynamic expansion turbine separate from the second dynamic expansion turbine; - conveying the first stream of heated refrigerant obtained at the outlet of the first heat exchanger to a first compression device without passing through the second heat exchanger and without passing through the third heat exchanger; - conveying the second stream of heated refrigerant issuing from the second heat exchanger to a second compression device without passing through the first heat exchanger and without passing through the third heat exchanger; - conveying the third stream of heated refrigerant issuing from the third heat exchanger to a third compression device without passing through the first heat exchanger and without passing through the second heat exchanger, characterized in that the first refrigerant stream is a substantially gaseous refrigerant, the latter stream being produced in a first refrigeration cycle from a first gaseous stream of expanded refrigerant fluid issuing from a first dynamic expansion turbine; the second dynamic expansion turbine being separate from the first dynamic expansion turbine; the third dynamic expansion turbine being separate from the first dynamic expansion turbine, and in that the first heat exchanger contains only two fluids. - precooling the natural gas feed stream by passing it through a first heat exchanger in order to obtain a feed stream precooled to a temperature below -20°C; - liquefying the precooled feed stream by passing it through a second heat exchanger in order to obtain at least one liquefied natural gas stream at a temperature below -80°C; - subcooling the liquefied natural gas stream by passing it through a third heat exchanger in order to obtain a liquefied natural gas stream subcooled to a temperature below -120°C; - placing the feed stream in a heat exchange relationship in the first heat exchanger with a first stream of refrigerant; - placing the precooled feed stream in a heat exchange relationship in the second heat exchanger with a second stream of gaseous refrigerant circulating in a second refrigeration cycle, the second gaseous refrigerant stream being produced from a second gaseous stream of expanded fluid coming from a second dynamic expansion turbine; - placing the liquefied natural gas stream in a heat exchange relationship in the third heat exchanger with a third refrigerant stream circulating in a third refrigeration cycle, the third refrigerant stream being produced at least partly from a third gaseous stream of expanded fluid issuing from a third dynamic expansion turbine separate from the second dynamic expansion turbine; - conveying the first stream of heated refrigerant obtained at the outlet of the first heat exchanger to a first compression device without passing through the second heat exchanger and without passing through the third heat exchanger; - conveying the second stream of heated refrigerant issuing from the second heat exchanger to a second compression device without passing through the first heat exchanger and without passing through the third heat exchanger; - conveying the third stream of heated refrigerant issuing from the third heat exchanger to a third compression device without passing through the first heat exchanger and without passing through the second heat exchanger,