In reality, humans are always exposed to a combination of toxic substances and seldom to a single agent. Simultaneous exposure to a multitude of chemicals could result in unexpected consequences. The combined risk may lead to greater or less than a simple summation of the effects induced by chemicals given individually. Here, a method is proposed for estimating the cumulative risk which is the risk associated with exposure to more than one chemical through different routes. The method is based on using the data to determine a suitable power transformation of the dose of each component of the mixture and fitting a dose­response model to the mixture under dose­addition. Necessary and sufficient conditions for the constancy of the relative potency between two chemicals in terms of the slopes of their corresponding dose­response models are derived and it is shown how the relative potency may be estimated directly from the joint dose­response model of the mixture. An example using a mixture of four chemicals is used for illustration.