We consider autonomous integrals F[u] := ∫Ω f(Du) dx for u: ℝn ⊃ Ω → ℝN in the multidimensional calculus of variations, where the integrand f is a strictly W1,p-quasiconvex C2-function satisfying the (p,q)-growth conditions γ|A|p ≤ f(A) ≤ Γ(1+|A|q) for every A ∈ ℝnN with exponents 1 < p ≤ q < ∞. Under these assumptions we establish an existence result for minimizers of F in W1,p(Ω;ℝN) provided q < np/(n-1) . We prove a corresponding partial C1,α-regularity theorem for q < p+min{2,p}/(2n). This is the first regularity result for autonomous quasiconvex integrals with (p,q)-growth.