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We report on the primary frequency standard now under construction at the Observatoire de Neuchatel (ON). The design is based on a continuous fountain of laser-cooled cesium atoms, which combines two advantages: the negligible contribution of collisions to the inaccuracy and the absence of stability degradation caused by aliasing effects encountered in pulsed operation. The design is reviewed with special emphasis on the specific features of a continuous fountain, namely the source, the microwave cavity (TE/sub 021/ mode), and the microwave modulation scheme. The possible sources of frequency biases and their expected contributions to the error budget are discussed. Based on present data, an accuracy in the low 10/sup -15/ range and a short-term stability of 7/spl middot/10/sup -14/ are attainable simultaneously under the same operating conditions.