There is given a constrained plant P described by a partial differential equation (p.d.o.) in two variables,tandx. Owing to uncertainty,Pbelongs to a given sotP. Tliero are assigned tolerances on the system responsey∥t,xx) in rosponso to command inputr(t,x), to be achieved over the definedt, xintervals for allpεpFrequency-response methods in two complex variables S1and S2are used to synthesize the system. Those methods are two-variable generalizations of the quantitative design techniques developed for lumped uncertain plants. Detailed design examples are given for two cases : (1) linear, constant-coefficient p.d.e. plant defined on semi-infinitet, xwith zero boundary conditions ; (2) similar to (1) except for definition on finitex. The latter case is converted to a problem on two semi-infinite variablestand ψ(x) with coefficients which are functions of ψ. A synthesis technique for lumped, time-varying plants is adapted for this now problem. This method may be used for the general linear uncertain p.d.e. plant on finite or semi-infinite intervals. An important limitation of the technique is to systems which are causal in botht; andx.