The PLL is used in every wireless receiver to lock the phase of the incoming signal with that generated locally. In perfect signal reception scenarios, the response behaviour of PLL when used during signal acquisition is non-linear, while it is linear during signal tracking. However, the PLL behaviour is highly sensitive to the presence of in-band interfering signals, which cause the behaviour of PLL to be non-linear during both signal acquisition and tracking stages. For simulation purposes, the mathematical model of the PLL needs to include the interfering signals for accurate study of any receiver design. Typical mathematical models for studying and simulating the PLL response, in the presence of interfering signals, take account of the frequency and amplitude changes of the received signal. However, this paper proposes that these models omit necessary information about the phase-change present in the received signal caused by any in-band interfering signal. That is, our mathematical model shows this phase-change in the actual information data caused by the interfering in-band signals as well as the frequency and amplitude changes. MATLAB simulation results, using our model for a Costas PLL, show that the Costas PLL will be unstable for a period of up to 2.2 msec even when the normalised PLL detuning parameter is less than one. Therefore, our model can help designers to decide what to do during this period of instability; for example, to help a decision for reacquiring or continuing tracking the received signal as is.