Let S be a connected open subset of 2-sphere S2 which is identified with the extended plane R2 ∪ {∞}. We assume that S contains the n segments {1, 2, …, n} × [-1, 1]. An n-lace ℓ (in S) is the union ℓ1 ∪ … ∪ ℓn of disjoint simple arcs in S such that ∂ ℓi = {(i, 1), (π (i),-1)}, i = 1, …, n, for some permutation π of {1, 2, …, n}. In this paper we will do present mapping class group description of n-laces, and 1-lace in 1-punctured plane, and 2-laces in S2. We will also describe the isotropy subgroup of the trivial lace in [Formula: see text].