For an irrational number $$x\in [0,1)$$ x ∈ [ 0 , 1 ) , let $$x=[a_1(x), a_2(x),\ldots ]$$ x = [ a 1 ( x ) , a 2 ( x ) , … ] be its continued fraction expansion. Let $$\psi : \mathbb {N} \rightarrow \mathbb {N}$$ ψ : N → N be a function with $$\psi (n)/n\rightarrow \infty $$ ψ ( n ) / n → ∞ as $$n\rightarrow \infty $$ n → ∞ . The (upper, lower) fast Khintchine spectrum for $$\psi $$ ψ is defined as the Hausdorff dimension of the set of numbers $$x\in (0,1)$$ x ∈ ( 0 , 1 ) for which the (upper, lower) limit of $$\frac{1}{\psi (n)}\sum _{j=1}^n\log a_j(x)$$ 1 ψ ( n ) ∑ j = 1 n log a j ( x ) is equal to 1. The fast Khintchine spectrum was determined by Fan, Liao, Wang, and Wu. We calculate the upper and lower fast Khintchine spectra. These three spectra can be different.