We consider a class of invariant sequential procedures for constructing one sided and two sided confidence sets for a parameter γ in Rk, with the property that they have a coverage probability at least 1 ‒a and probability of covering a certain set of false values at most β. The asymptotic properties of the stopping time are studied and the limiting values of the error probabilities are found as the parameter approaches the boundary points. Applications are made to the problem of simultaneous confidence sets for the mean and variance of a normal random vari¬able and for its multivariate analogue.