The paper demonstrates a new approach to identify healthy calves (“healthy”) and naturally occurring infectious bronchopneumonia (“sick”) calves by analysis of the gaseous phase over nasal secretions using 16 piezoelectric sensors in two portable devices. Samples of nasal secretions were obtained from 50 red-motley Holstein calves aged 14–42 days. Calves were subjected to rectal temperature measurements, clinical score according to the Wisconsin respiratory scoring chart, thoracic auscultation, and radiography (Carestream DR, New York, USA). Of the 50 calves, we included samples from 40 (20 “healthy” and 20 “sick”) in the training sample. The remaining ten calves (five “healthy” and five “sick”) were included in the test sample. It was possible to divide calves into “healthy” and “sick” groups according to the output data of the sensor arrays (maximum sensor signals and calculated parameters Ai/j) using the principal component linear discriminant analysis (PCA–LDA) with an accuracy of 100%. The adequacy of the PCA–LDA model was verified on a test sample. It was found that data of sensors with films of carbon nanotubes, zirconium nitrate, hydroxyapatite, methyl orange, bromocresol green, and Triton X-100 had the most significance for dividing samples into groups. The differences in the composition of the gaseous phase over the samples of nasal secretions for such a classification could be explained by the appearance or change in the concentrations of ketones, alcohols, organic carboxylic acids, aldehydes, amines, including cyclic amines or those with a branched hydrocarbon chain.