It is known that unbiased estimates of the relative risk in a cohort study may be obtained by a matched case-control analysis that compares each case with a random sample of controls obtained from those at risk at the time of case incidence. Through inadvertence , or for practical or scientific reasons, a biased referent group may be selected instead. Three kinds of biasing restrictions on controls are commonly imposed: (i) the requirement that controls remain completely disease-free for a fixed time interval, (ii) the exclusion of all cases incident during observation as controls, and (iii) the exclusion, from the referent group, of subjects who develop other diseases, which may be related to the exposure of interest. The bias in estimation of the relative risk associated with each of these restrictions is evaluated under the proportional-hazards model. For several examples of cancer mortality data, the bias from (iii) appears quite small, whereas the bias from (i) can be appreciable and is mostly attributable to the bias from case exclusion (ii). The effect of random variation in the time of onset of exposure is to reduce these biases.