[en] Dimensional regularisation is used to calculate the determinant of small oscillations about instanton solutions in g(phi⁴)₄ field theories with g < 0. Principal features of the method are: (i) the known instanton solution of four dimensions may be used even though it is not a solution of the regularised theory; (ii) the minimally subtracted renormalised coupling can be introduced directly. Results are also given for 0(n) internal symmetry and conformal invariant phisup(2N) theories (g < 0). The high-order estimates obtained agree with those of previous workers. (author)