I'm not pregnant and i'm taking alesse. is it normal for your period to just stop completely?

It happens: After being on the pills for awhile, flow can get lighter or even stop, but if pregnancy is a possibility, so do a test. If the test is negative, it's not medically a problem not to have a period. But no birth control is perfect. The failure rate of the pill in typical use in 9% (9/100 women get pregnant in first year), but in perfect use (no missed pills, etc) it's <1%.