The conventional first-order linear differential equation for the partial pressures of the residual gases in an ultrahigh vacuum system has been tested experimentally and found to be satisfactory for He,CH4,N2, and Ar but unsatisfactory forH2and CO. Two simultaneous first-order linear differential equations, based upon a model postulating a surface phase obeying Henry’s Law, are suggested forH2and CO. The solutions to these simultaneous equations yield greatly improved but not complete agreement with experiment. Qualitative suggestions are made for further improvement of the model. Literature concerning quantitative measurements ofH2and CO in ultrahigh vacuum systems and based upon the conventional pressure equation is reexamined critically in terms of the new system of equations.