The Wiener-Hopf technique is applied to solve the linearized problem of a two-dimensional compound gas jet, i.e. a jet embedded in a gaseous stream of finite width. The solution is found for all combinations of supersonic and subsonic flows in jet and stream. The general nature of the solution when only one of the flows is supersonic varies according as the value of a certain quantity mk, depending upon the gas constants, Mach numbers and widths of streams, is greater than or less than unity. When mk= 1 the solution appears to be invalid and it is suggested that, in this critical case, a steady flow (regarded as the limit in time of an unsteady flow) may not exist. It is further shown that the solution propounded by Pai (1952) for a supersonic jet embedded in a subsonic stream is simply the asymptotic form of the general solution. The findings of Pack (1956) for a supersonic jet in a supersonic stream are confirmed and extended.