An adaptor for connecting a medical container to a connector having a proximal region provided with connecting means at its proximal end, the adaptor comprising: a proximal part configured to be secured onto a distal tip of a medical container, a distal part configured to receive said proximal region of said connector in order to establish a fluid communication between the distal tip of the medical container and the connector, a plurality of longitudinal projections configured to engage said connecting means in an axial snap-fit relationship when the connector reaches a predetermined position in the adaptor, the plurality of longitudinal projections being distributed circumferentially on an inner surface of said distal part, the longitudinal projections comprising a distal portion configured to exert a progressively increasing radial pressure on said connecting means as the connector is moved axially proximally within the adaptor and a proximal portion configured to authorize the partial release of said pressure as the connector is moved further axially proximally, said proximal portion being further configured to be contacted by said connecting means upon said partial release of said pressure and to emit a sound when contacted by said connecting means, thereby providing an end user with a tactile and audible indication that the connection between the connector and the adaptor is secured, characterized in that the distal portion of the longitudinal projections comprises a first wall having a first radial thickness, the value of said first radial thickness increasing from a distal end of said distal portion to a proximal end of said distal portion, and the proximal portion comprises a second wall having a substantially constant second radial thickness, the value of said second radial thickness being greater than the value of said first radial thickness at the distal end of said distal portion and being less than the value of said first radial thickness at the proximal end of said distal portion. a proximal part configured to be secured onto a distal tip of a medical container, a distal part configured to receive said proximal region of said connector in order to establish a fluid communication between the distal tip of the medical container and the connector, a plurality of longitudinal projections configured to engage said connecting means in an axial snap-fit relationship when the connector reaches a predetermined position in the adaptor, the plurality of longitudinal projections being distributed circumferentially on an inner surface of said distal part, the longitudinal projections comprising a distal portion configured to exert a progressively increasing radial pressure on said connecting means as the connector is moved axially proximally within the adaptor and a proximal portion configured to authorize the partial release of said pressure as the connector is moved further axially proximally, said proximal portion being further configured to be contacted by said connecting means upon said partial release of said pressure and to emit a sound when contacted by said connecting means, thereby providing an end user with a tactile and audible indication that the connection between the connector and the adaptor is secured, characterized in that the distal portion of the longitudinal projections comprises a first wall having a first radial thickness, the value of said first radial thickness increasing from a distal end of said distal portion to a proximal end of said distal portion, and the proximal portion comprises a second wall having a substantially constant second radial thickness, the value of said second radial thickness being greater than the value of said first radial thickness at the distal end of said distal portion and being less than the value of said first radial thickness at the proximal end of said distal portion.