In the last decades, the technological development has generated constant and important cultural and economic changes around the world, creating a gap between the people that have and know how to use the technology and those who do not. This gap, known as digital gap, affects countries and cities, whose leaders every time are more conscious of the needing of entering to the knowledge society and for doing it, they speak about the necessity of creating public policies that help them in their intention. The leaders of the city of Medellin have not been out to this call, and from middle of the decade of the 90, they began to do efforts to include the technology in the processes of the city, specially from the educational area. This article tends then, to make an approximation, throughout the systematizing, to the public policies on Technologies of Information and Communication, TIC, developed by the Medellin City Hall in the period 2001-2007, and its influence in the offers of training in the use and appropriation of TIC for the training of the citizens. The systematizing sustained with a wide documentary investigation and interviews to the people in charge of the creation of the programs on TIC in Medellin in the selected period, allowed to conclude that in spite of the efforts done by the municipal administrations, Medellin still does not get to have a public policy on TIC. This implies that towards the future the citizens don’t have guaranteed the continuity in the appropriation process lead by the Municipal Administrations, delaying this way the arrival of the city to the knowledge society. The most nearby thing to a public policy on TIC in Medellin is Medellin Digital, an inter-institutional initiative lead by the Municipal Administration, which from the year 2006 is gathering and coordinating all the processes of technological access, use and appropriation of the city, but that does not have a strategy that allows it to remain in spite of the political changes. From the political area it can be found three explanations in order to explain why do not exist a public policy on TIC in Medellin: The lack of interest on TIC of some sectors, the changes of political ideologies in the administration that has prevented the continuity of some proposals; and few clarity of the concept and the way of constructing public policies that have some leaders.