We introduce Markov-like functions on intervals as a generalization of generalized Markov interval functions and define the notation of the same pattern between Markov-like functions. Then we show that two generalized inverse limits with Markov-like bonding functions having the same pattern are homeomorphic. This result gives a generalization of the results of S. Holte ([9]) and I. Banič and T. Lunder ([5]). ←− {X n , f n } of the inverse sequence {X n , f n } n∈N is defined by lim ←− {X n , f n } := {(x 1 , x 2 ,. . .) ∈ ∞ n=1 X n | x n ∈ f n (x n+1) for any n ∈ N}.

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