15. At least another 7 weeks
15.【Solution】Let at least $\mathrm{n}$ weeks pass, it is possible to rest on the $\mathrm{n}$th Saturday, or it is also possible not to rest on the $\mathrm{n}$th Saturday (resting for 2 days on Sunday and Monday), the former yields: $7 \mathrm{n}-2=10 \mathrm{~K}+8(1)$, the latter yields: $7 \mathrm{n}-1=10 \mathrm{~K}+8(2)$, where $\mathrm{K}$ is a natural number.
(1) That is, $7 n=10(K+1)$, thus, $n$ is a multiple of 10, at least 10.
(2) That is, $7 n=10 K+9$, it indicates that the unit digit of $7 n$ is 9, so $n=7,17, \cdots$

Therefore, at least another 7 weeks must pass before resting on a Sunday again.
15. Master Wang works in a special position, where he works for 8 consecutive days and then takes 2 consecutive days off. If he is off on this Saturday and Sunday, then, at least how many weeks later will he be off on a Sunday again?