In this paper we discuss some of the obstacles to the construction of credible models of tritium transport for use in dose assessments. We illustrate these difficulties by comparing model predictions of environmental tritium levels with measurements. Environmental monitoring of tritium has shown that specific activities in precipitation over land are typically higher by a factor of three to four than those in precipitation over the oceans. Experience with modeling CO2 turnover in the oceans has led to the conclusion that two-box reservoir models of the ocean often give unsatisfactory representations of transient solutions. Failure to consider these factors in global models can lead to distorted estimates of collective dose and create difficulties in validation of the model against real data. We illustrate these problems with a seven-box model recommended by the National Council on Radiation Protection and Measurements (NCRP), in which we forced the atmospheric compartment to reproduce an exogenous function based on historic observations of HTO in precipitation at 50°N. The ocean surface response overestimates tritium data from the surface waters of the Northern Atlantic by a factor of about three, and the fresh water response underestimates data from the Ottawa River by nearly an order of magnitude. Revision of the model to include (1) separate over-land and over-ocean compartments of the atmosphere and (2) a box-diffusion model of the subsurface ocean brings the discrepant responses into good agreement with the environmental data. In a second exercise, we used a latitudinally disaggregated model and replaced a tropospheric compartment in the northern hemisphere by historic precipitation data. The model's response greatly underestimates the tritium specific activity in the southern hemisphere. The large discrepancy probably indicates that much of the release from weapons testing occurred in the stratosphere and that a significant fraction of the release occurred as HT rather than HTO. These exercises lead us to doubt that a proper global transport model for tritium is available at present for collective dose assessment.