We report on magnetic and magnetoresistance measurements in two categories of superconducting Nb films grown via magnetron sputtering and MgB−2 bulk samples. In the first category, films of Tc = 9.25 K were produced by annealing during deposition. In these films, the magnetic measurements exhibited the so-called "second magnetization peak" ("SMP"), which is accompanied by thermomagnetic instabilities (TMI). The characteristic field H fj , where the first flux jump occurs, has been studied as a function of the sweep rate of the magnetic field. Interestingly, in the regime T < 6.4 K, the respective line H fj (T ) is constant, H fj (T< 6.4 K)= 40 Oe. A comparison to TMI observed in MgB2 bulk samples is also performed. Our experimental findings can't be described accurately by current theories on TMI. In the second category, films of Tc = 8.3 K were produced without annealing during deposition. In such films, we observed a peak effect (PE). In high magnetic fields the PE is accompanied by a sharp drop and a narrow hysteretic behavior (∆T < 20 mK) in the measured magnetoresistance. In contrast to experimental works presented in the past, the comparison of our magnetic measurements with the magnetoresistance data suggests that rather the appearance of surface superconductivity than the melting transition of vortex matter, is the cause of the observed behavior.