IBM System/3 and the System/360 Model 20. Multi-leaving is "fully synchronous, pseudo-simultaneous, bi-directional transmission of a variable number of data streams between two or more computers utilizing binary-synchronous communications facilities."

Third party vendors developed a variety of 2770/2780/3780 simulators and Multi-leaving implementations for use with HASP and ASP. Some of these vendors incorrectly referred to their products as HASP