Abstract Salient auditory stimuli typically exhibit rhythmic temporal patterns. A growing body of evidence suggests that, in primary auditory cortex (A1), attention is associated with entrainment of delta rhythms (1 – 4 Hz) by these auditory stimuli. It is thought that this entrainment involves phase reset of ongoing spontaneous oscillations in A1 by thalamus matrix afferents, but precise mechanisms are unknown. Furthermore, naturalistic stimuli can vary widely in terms of their rhythmicity: some cycles can be longer than others and frequency can drift over time. It is not clear how the auditory system accommodates this natural variability. We show that in rhesus macaque monkey A1 in vivo , bottom-up gamma (40 Hz) click trains influence ongoing spontaneous delta rhythms by inducing an initial delta-timescale transient response, followed by entrainment to gamma and suppression of delta. We then construct a computational model to reproduce this effect, showing that transient thalamus matrix activation can reset A1 delta oscillations by directly activating deep (layer 5) IB cells, promoting bursting, and beginning a new delta cycle. In contrast, long duration gamma-rhythmic input stimuli induce a steady-state containing entrainment of superficial RS and FS cells at gamma, and suppression of delta oscillations. This suppression is achieved in the model by two complementary pathways. First, long-duration thalamus matrix input causes IB cells to switch from bursting to sparse firing, which disrupts the IB bursts associated with delta. Second, thalamus core input activates deep FS cells (by way of layer 4), which fire at gamma frequency and actively inhibit the delta oscillator. Together, these two fundamental operations of reset and suppression can respectively advance and delay the phase of the delta oscillator, allowing it to follow rhythms exhibiting the type of variability found in the natural environment. We discuss these findings in relation to functional implications for speech processing. Author summary Neurons organize their firing into synchronous, rhythmic patterns. These neural oscillations have been shown to entrain to rhythmic stimuli in the external world, such as patterns of speech or patterns of movement. By entraining to a particular input stimulus, these oscillations are thought to help us attend to that stimulus and to exclude others. To understand how this synchronization emerges, we constructed a physiologically detailed mathematical model of the primary auditory cortex. By fitting this model to a variety of experimental data, we suggest fundamental mechanisms by which neurons of the auditory cortex can synchronize their activity to rhythmic external stimuli. This result will be useful for understanding the mechanism and limitations of oscillatory entrainment, which are thought to underlie the processing of naturalistic auditory inputs like speech or music. Furthermore, this model, though simplified, was shown to generalize and reproduce a wide range of experimental results, and can thus be used as a starting point for building more complex models of auditory cortex.