The problem of constructing a Hurwitz polynomial Â(s) of degreen, under the condition that the coefficients up to and including that of 8m−1are given, is discussed, Root locus arguments are used to establish necessary and sufficient conditions for stabilizability withm= l, 2, 3 and sufficient conditions form> 3. A Routh array approach yields necessary and sufficient conditions form= 4 and a general method of attack form> 4 The origin of the problem (in the design of tracking servo-mechanisms) is explained, and a procedure for producing a system with specified type number is outlined.