The importance of reliable record linkage for high quality-population-based disease registration is widely recognized. Systematic methodologic work is lacking, however, on the effects of record linkage errors on the use of disease registries for epidemiologic purposes. The present paper provides algebraic models describing the effects of record linkage errors on monitoring survival of registered patients, which is commonly performed by matching registry records against a database of death certificates, and on registry-based incidence follow-up of external cohorts. Homonym errors, that is, erroneous linkage of records that pertain to distinct individuals, lead to underestimation of survival of registered patients and to overestimation of disease incidence among external cohorts linked to the registry, while synonym errors, that is, failure to link notifications on the same individual, have opposite effects. The magnitude of effects of record linkage errors are illustrated with numerical examples.