For an integer k 2, let .F.k/ n / n be the k-Fibonacci sequence which starts with 0; : : : ; 0; 1 (k terms) and each term afterwards is the sum of the k preceding terms.In this paper, we search for powers of 2 which are sums of two k-Fibonacci numbers.The main tools used in this work are lower bounds for linear forms in logarithms and a version of the Baker-Davenport reduction method in diophantine approximation.This paper continues and extends the previous work of [4] and [2].