It is currently assumed that infrared dark clouds (IRDCs) represent the earliest evolutionary stages of high-mass stars (>8 M⊙). Submillimeter and millimeter-wave studies performed over the past 15 yr show that IRDCs possess a broad variety of properties, and hence a wide range of problems and questions that can be tackled. In this paper, we report an investigation of the molecular composition and chemical processes in two groups of IRDCs. Using the Mopra, APEX, and IRAM radio telescopes over the last four years, we have collected molecular line data for CO, H2CO, HNCO, CH3CCH, CH3OH, CH3CHO, CH3OCHO, and CH3OCH3. For all of these species we estimated molecular abundances. We then undertook chemical modeling studies, concentrating on the source IRDC028.34+0.06, and compared observed and modeled abundances. This comparison showed that to reproduce observed abundances of complex organic molecules, a zero-dimensional gas-grain model with constant physical conditions is not sufficient. We achieved greater success with the use of a warm-up model, in which warm-up from 10 K to 30 K occurs following a cold phase.