In Phase III clinical trials, ethical considerations often demand interim analyses in order that the better treatment be made available to all patients as soon as possible. Group sequential test designs that do not treat the hypotheses symmetrically may not fully address this concern since early termination of the study may be easier under one of the hypotheses. We present a one-parameter family of symmetric one-sided group sequential designs that are nearly fully efficient in terms of the average sample number. The symmetric tests are then extended to a two-sided hypothesis test. These symmetric two-sided group sequential tests are found to have improved overall efficiency when compared to the tests proposed by Pocock (1977, Biometrika 64, 191-199) and O'Brien and Fleming (1979, Biometrics 35, 549-556). Tables of critical values for both one-sided and two-sided symmetric designs are provided, thus allowing easy determination of sample sizes and stopping boundaries for a group sequential test. Approximate tests based on these designs are proposed for use when the number and timing of analyses are random.