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We apply the method of QCD sum rules to study the doubly heavy tetraquarkstates $QQ\bar{q}\bar{n}$ with spin-parity $J^{P}=1^{+}$ and strangeness $S=0,-1$ using careful estimates of the Borel and threshold parameters involved.Masses of the doubly bottom and charmed tetraquarks with isospin $I=0,1/2, 1$are computed precisely via taking into account multifarious condensates up todimension $10$. Comparing with the two-heavy meson thresholds, we find that allnonstrange doubly-bottom tetraquarks and a doubly-charmed tetraquarks associtedwith $J_{3}$ with $J^{P}=1^{+}$ are stable against strong decay into two bottommesons while a doubly-charmed tetraquarks associated with current $J_{2}$ isunstable against strong decay. By the way, weak decay widths of the doublybottom tetraquarks are also given.

Masses of doubly heavy tetraquarks $QQ\bar{n}\bar{q}$ with $J^{P}=1^{+}$