I am using the cleanser, then acne gel, then Hydroxy gel then the rejuvenating and repair gel followed with moisturizer. I am worried that I’m applying the next gel too soon or is it fine if skin is dry to apply the next gel.

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You are correct to apply the next step as soon as the previous one has drawn in.  The Acne Gel need not become a permanent part of the daily routine, but up to 2 weeks at a time, stop for a while and re-apply when acne re-appears. The remaining products are perfect for the routine..