A method for sequentially extracting essential oil, incensole derivatives and boswellic acid from frankincense resin, said method comprising the steps of: a) grinding the frankincense resin; b) separating a first fraction of essential oil with liquid carbon dioxide at a first temperature ranging between 0 °C and 30 °C and a first pressure ranging between 40 bars and 73.8 bars or with mild supercritical carbon dioxide, and with a first flow rate ranging between 10g and 400g/kg ground material/min until no further essential oil can be recovered or the extract yield falls below 0.1 % of starting mass per hour; c) retrieving essential oil from the separator; d) separating a second fraction of incensole derivatives with supercritical carbon dioxide at a second temperature ranging between 31 °C and 100°C and a second pressure of at least 72.8 bars and a second flow rate ranging between 10g and 400g/kg ground material/min until no further incensole or its derivatives can be recovered or the extract yield falls below 0.1% of starting mass per hour; e) retrieving incensole derivatives from the separator; f) optionally, continuing the separation process with supercritical carbon dioxide at other sets of increasing temperature and/or pressure until further desired fractions are separated; g) separating a further fraction of boswellic acid with supercritical carbon dioxide at a temperature of at least 31 °C and a pressure of at least 72.8 bars and a flow rate ranging between 10g and 400g/kg ground material/min using a co-solvent at a level ranging between 0.05 vol% and 50.0 vol% of the CO 2 flowrate until complete separation of boswellic acids is achieved or it is determined that no further materials can be extracted or the extract yield falls below 0.1 % of starting mass per hour; h) retrieving boswellic acid from the separator and removing the co-solvent by evaporation or distillation; i) optionally, continuing the separation process with supercritical carbon dioxide at another set of temperature and pressure and co-solvent until all desired fractions are separated; j) retrieving the remaining unseparated residues. a) grinding the frankincense resin; b) separating a first fraction of essential oil with liquid carbon dioxide at a first temperature ranging between 0 °C and 30 °C and a first pressure ranging between 40 bars and 73.8 bars or with mild supercritical carbon dioxide, and with a first flow rate ranging between 10g and 400g/kg ground material/min until no further essential oil can be recovered or the extract yield falls below 0.1 % of starting mass per hour; c) retrieving essential oil from the separator; d) separating a second fraction of incensole derivatives with supercritical carbon dioxide at a second temperature ranging between 31 °C and 100°C and a second pressure of at least 72.8 bars and a second flow rate ranging between 10g and 400g/kg ground material/min until no further incensole or its derivatives can be recovered or the extract yield falls below 0.1% of starting mass per hour; e) retrieving incensole derivatives from the separator; f) optionally, continuing the separation process with supercritical carbon dioxide at other sets of increasing temperature and/or pressure until further desired fractions are separated; g) separating a further fraction of boswellic acid with supercritical carbon dioxide at a temperature of at least 31 °C and a pressure of at least 72.8 bars and a flow rate ranging between 10g and 400g/kg ground material/min using a co-solvent at a level ranging between 0.05 vol% and 50.0 vol% of the CO 2 flowrate until complete separation of boswellic acids is achieved or it is determined that no further materials can be extracted or the extract yield falls below 0.1 % of starting mass per hour; h) retrieving boswellic acid from the separator and removing the co-solvent by evaporation or distillation; i) optionally, continuing the separation process with supercritical carbon dioxide at another set of temperature and pressure and co-solvent until all desired fractions are separated; j) retrieving the remaining unseparated residues.