For N ∈ N≥2 and α ∈ R such that 0 < α ≤ N − 1, the continued fraction map Tα: [α, α+1] → [α, α+1) is defined as Tα (x):= N/x−d(x), where d: [α, α+1] → N is defined by d(x):= ⌊N/x − α⌋. A maximal open interval (a, b) ⊂ Iα is called a gap of Iα if for almost every x ∈ Iα there is an n0 (x) ∈ N such that xn /∈ (a, b) for all n ≥ n0 . In this paper, all conditions are given in which Iα is gapless. For α =√N − 1 it is shown that the number of gaps is a finite, monotonically non-decreasing and unbounded function of N.@en