The availability of heterogeneous CPU+GPU systems has opened the door to new opportunities for the development of parallel solutions to tackle complex biological problems. The reconstruction of evolutionary histories among species represents a grand computational challenge, which can be addressed by exploiting this kind of hardware designs. In this research, we study the application of heterogeneous computing with OpenCL to accelerate one of the most well-known objective functions for inferring phylogenies, the phylogenetic parsimony function. For this purpose, we undertake the design of CPU and GPU kernel implementations of this relevant function, proposing a heterogeneous CPU+GPU multidevice approach that distributes multiple parsimony evaluations among processing devices. Experiments on 6 real nucleotide data sets and comparisons with other parallel implementations give account of the benefits of the proposal in this paper, obtaining significant parallel results by combining CPU and GPU capabilities in accordance with the characteristics of the input data.