The use of multiple dyes during histological sample preparation can reveal distinct tissue properties. However, since the slide preparation differs for each dye, the tissue slides are being deformed and a nonrigid registration is required before further processing. The registration of histology images is complicated because of: (i) a high resolution of histology images, (ii) complex, large, nonrigid deformations, (iii) difference in the appearance and partially missing data due to the use of multiple dyes. In this work, we propose a multistep, automatic, nonrigid image registration method dedicated to histology samples acquired with multiple stains. The proposed method consists of a feature-based affine registration, an exhaustive rotation alignment, an iterative, intensity-based affine registration, and a nonrigid alignment based on modality independent neighbourhood descriptor coupled with the Demons algorithm. A dedicated failure detection mechanism is proposed to make the method fully automatic, without the necessity of any manual interaction. The described method was proposed by the AGH team during the Automatic Non-rigid Histological Image Registration (ANHIR) challenge. The ANHIR dataset consists of 481 image pairs annotated by histology experts. Moreover, the ANHIR challenge submissions were evaluated using an independent, server-side evaluation tool. The main evaluation criteria was the target registration error normalized by the image diagonal. The median of median target registration error is below 0.19%. The proposed method is currently the second-best in terms of the average ranking of median target registration error, without statistically significant differences compared to the top-ranked method. We provide an open access to the method software and used parameters, making the results fully reproducible.