We present a detailed study of the recently reported resistance peaks close to the superconducting transition of quasi-one-dimensional mesoscopic Al structures. It is found that the anomalies can be induced by radio-frequency irradiation or by applying sufficiently high dc currents. The nonmonotonic resistance curves are correlated with excess voltages in the voltage-current characteristics close to the critical current and depend strongly on the temperature and the magnetic field. The experimental results can be qualitatively understood in terms of charge imbalance around phase-slip centers which nucleate at particular spots in the sample with a locally reduced transition temperature. [S0163-1829(98)05717-8].