An adaptor for connecting a drug delivery device to a needleless access device having a straight external thread, including engagement means for mounting said adaptor on the drug delivery device, and an internal thread intended to cooperate with said external thread on a determined length, said internal thread showing on a distal part of said length a first major diameter mating that of said straight external thread, wherein said internal thread shows on a proximal part of said length a second major diameter, where the second major diameter is strictly smaller than the first major diameter, said internal thread further including a tapered portion linking said proximal part to said distal part.