Streamer discharges are often operated in a repetitively pulsed mode and are therefore influenced by species left over from the previous discharge, especially free electrons and ions. We have investigated these effects by applying two consecutive positive high voltage pulses of 200-700 ns duration to a point plane gap in artificial air, pure nitrogen, other nitrogen-oxygen mixtures and pure argon at pressures between 67 and 533 mbar. The pulses had pulse-to-pulse intervals ({\Delta}t) between 200 ns and 40 ms. We imaged both discharges with two ICCD cameras and combined this to a compound image. We observe for values of {\Delta}t below 0.5-15 {\mu}s (at 133 mbar, depending on gas mixture) that during the second pulse the streamers continue the paths of the first-pulse streamers. We call the maximal time for which this continuation still occurs the continuation time. For N\(_{2}\) - O\(_{2}\) mixtures, this time has a maximum at an oxygen concentration of about 0.2%. According to our plasma chemical modelling this maximum is determined by the electron loss rate which has a minimum around this oxygen concentration. Depending on oxygen concentration the dominant recombining positive ion is N\(_{4}^{+}\), O\(_2^+\) or O\(_{4}^{+}\) where O\(_{2}^{+}\) dominates around 0.2% O\(_{2}\) and recombines slowest. For increasing values of {\Delta}t we observe that after the continuation phase first no new streamers occur at all, then new streamers show up that avoid the entire pre-ionized region. Next we see new thin streamers that follow the edges of the old channels. For larger {\Delta}t (10-200 {\mu}s) the new streamers start to increase in size and move to the centre of the old channel. Finally, around millisecond timescales the new channels are completely independent of the old channels.