In examining genetic data in recent publications, Backeljau et al. showed cases in which two or more different trees (tie trees) were constructed from a single data set for the neighbor-joining (NJ) method and the unweighted pair group method with arithmetic mean (UPGMA). However, it is still unclear how often and under what conditions tie trees are generated. Therefore, I examined these problems by computer simulation. Examination of cases in which tie trees occur shows that tie trees can appear when no substitutions occur along some interior branch(es) on a tree. However, even when some substitutions occur along interior branches, tie trees can appear by chance if parallel or backward substitutions occur at some sites. The simulation results showed that tie trees occur relatively frequently for sequences with low divergence levels or with small numbers of sites. For such data, UPGMA sometimes produced tie trees quite frequently, whereas tie trees for the NJ method were generally rare. In the simulation, bootstrap values for clusters (tie clusters) that differed among tie trees were mostly low (< 60%). With a small probability, relatively high bootstrap values (at most 70%-80%) appeared for tie clusters. The bias of the bootstrap values caused by an input order of sequence can be avoided if one of the different paths in the cycles of making an NJ or UPGMA tree is chosen at random in each bootstrap replication.