In this paper, we study the properties of the generalized harmonic numbers H_n,k,r(α,β). In particular, by means of the method of coefficients, generating functions and Riordan arrays, we establish some identities involving the numbers H_n,k,r(α,β), Cauchy numbers, generalized Stirling numbers, Genocchi numbers and higher order Bernoulli numbers. Furthermore, we obtain the asymptotic values of some summations associ- ated with the numbers H_n,k,r(α,β) by Darboux's method and Laplace's method.