This paper uses fractional integration and cointegration for the period of January 2000-June 2018 to investigate the stochastic properties of the bilateral linkages between stock markets in Africa and selected international markets to establish if markets in Africa co-move with the rest of the world. Results from the univariate analysis show that there exists a high degree of persistence with orders of integration about 1 or higher than 1, implying that shocks to these stock markets have significant permanent effects. Concerning bivariate results and testing for cointegration, evidence of cointegration is found for Egypt and Kenya against the UK and the Europe Zone. There are some other cases where partial evidence of cointegration is found, though in general, in all cases, we observe that the degree of cointegration is very low, implying very long periods of convergence. (C) 2018 Africagrowth Institute. Production and hosting by Elsevier B.V.