The "permanent" unemployment concept of Rueff [1925, 1931] represents a. form of equilibrium unemployment dye to a downward wage rigidity leading to a persistent excess of real wage compared to its value corresponding to a competitive equilibrium. Relative to this known aspect of the Rueff's contribution, this paper shows that the author considered also a "temporary" unemployment due to an insufficient level of the economic activity, and a "minimum" frictional unemployment prevailing in the normal functioning of any economy. Using empirical data in England during the 1920's, Rueff suggested that the "permanent" component was the main explanation of the unemployment (this is the so-called "law of Rueff"). We conduct simple econometric tests using Rueff's data that confirm this conclusion, and we show that releasing the assumption of a constant labor productivity (that was supposed by Rueff) improves the accuracy of the "law of Rueff". In line with these results, we show that the theoretical approach proposed by Allais [19431 joins the three types of unemployment pointed out by Rueff, renamed as "chronic", "conjonctural" and "technological", respectively. Much later, Allais [1980] proposed an unrecognized straightforward econometrical equation comprising these three types of unemployment to represent the french unemployment over the period 1952-78. We confirm that this equation describes a large part of the evolution of unemployment in England during the 1920's and in France during the period 1970-2008, but the properties of residuals show that this equation is mis-specified. Finally, we suggest that, under some restrictive conditions, the three types of unemployment distinguished by Rueff and Allais can be seen through the equilibrium unemployment defined by the imperfect competition WS -PS model (Layard-Nickel-Jackman [1991]), hence allowing to indicate why the Allais' equation is misspecified, thus highlighting the important scientific advances that have been made since.The "permanent" unemployment concept of Rueff [1925, 1931] represents a. form of equilibrium unemployment dye to a downward wage rigidity leading to a persistent excess of real wage compared to its value corresponding to a competitive equilibrium. Relative to this known aspect of the Rueff's contribution, this paper shows that the author considered also a "temporary" unemployment due to an insufficient level of the economic activity, and a "minimum" frictional unemployment prevailing in the normal