Fredwina,
Some possibile causes?:
Did you use a potting soil made for cacti?- often those have way too much peat moss in them and it prevents the soil from getting wet at all. Most cactus growers mix regular potting soil and some sort of sand or tiny gravel about 1/2 and 1/2- that mixture works well.
Also, if you have just repotted, the plants will be under stress and should not be in the blasting sun all day for a while. Cactus need to adjust gradually from indoors to out in the full sun. Too sudden a change can actually burn them.
Don't let them get water more than once every week or two...they rot easily in soil that is not allowed to dry out between waterings.