In experiments with paired comparisons, judges are occasionally allowed to express indifference between alternatives. For the analysis of such data, models for paired comparisons with ties are needed. Several models with tie parameters are reviewed. All are extensions of the basic models of L. L. Thurstone (1927) and R. A. Bradley and M. E. Terry (1952). Some of these models can be reparameterized into an exponential family of distributions. This gives the attractive possibility of conditioning individual tie parameters out of the model so that the object parameters can be estimated independently of the tie parameters and with desirable asymptotic properties. In addition, focus is on the use of models with tie parameters for analyzing induced experiments with ties in which the original experiment has no ties, or even no comparisons. This technique may have considerable advantages over analyzing the original experiment, as is shown in the case of the Rasch model for binary test items. One data table and one figure are provided. (Author/SLD)