Abstarct: Abstract In this paper, the problem on best coapproximation in normed space is cosidered, and the concept best simultaneous coapproximation, and ε -simultaneous coapproximation are presented. Theory of coapproximation was first introduced in 1972 by Franchetti and Furi. Let X be a normed space with norm ∥ . ∥ ,let G be a nonempty subset of X and let x ∈ X . Then g0 ∈ G is called a best coapproximation from G to x if, ∥ g − g0 ∥≤∥ x − g ∥ (∀g ∈ G). The set of best coapproximation to x from G will be denoted RG(x). We also present the results concerning best uniform coapproximation in C[a, b].