The stabilization of second-order unstable delay processes by simple controllers is investigated. The elementary analysis based upon the Nyquist stability criterion is carried out to establish explicit and complete stabilizability results in terms of the upper limit of time-delay size and the computational methods for determining stabilizing controller parameters. The analysis provides both theoretical understanding of such stabilization problem and practical guidelines for actual controller design. The results for other unstable delay processes studied extensively in the literature are also obtained as the special cases of the above second-order one. (c) 2007 Elsevier Ltd. All rights reserved.