Time-resolved IR pump-probe (IR-PP) and two-dimensional IR (2D-IR) spectroscopy are valuable techniques for studying various ultrafast chemical and biological processes in solutions. The time-dependent changes of nonlinear IR signals reflecting fast molecular processes such as vibrational energy transfer and chemical exchange provide invaluable information on the rates and mechanisms of solvation dynamics and structural transitions of multispecies vibrationally interacting molecular systems. However, due to the intrinsic difficulties in distinguishing the contributions of molecule-specific processes to the time-resolved IR signals from those resulting from local heating, it becomes challenging to interpret time-resolved IR-PP and 2D-IR spectra exhibiting transient growing-in spectral components and cross-peaks unambiguously. Here, theoretical considerations of various effects of vibrational coupling, energy transfer, chemical exchange, the generation of hot ground states, molecular photothermal process, and their combinations on the line shapes and time-dependent intensities of IR-PP spectra and 2D-IR diagonal peaks and cross-peaks are presented. We anticipate that the present work will help researchers using IR pump-probe and 2D-IR techniques to distinguish local heating-induced photothermal signals from genuine nonlinear IR signals.