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We propose two scheduling and resource allocation schemes that deal with Quality of Service (QoS) requirements in Uplink Long Term Evolution (LTE) systems. QoS for a multiclass system has been seldom taken into account in previous resource allocation algorithms for LTE uplink. In one of the new algorithms, we investigate the possibility of assigning more than one resource block and its consequences on satisfying stringent QoS requirements in the context of heavy traffic, either in terms of end-to-end delays or of minimum rates. System capacity and the number of effectively served requests are used as performance metrics. Numerical results show that it is possible to manage a multiclass scheme while satisfying the QoS constraints of all requests. Allowing the assignment of more than one resource block per request did not appear to be a meaningful advantage. Indeed, it is only useful when there is a heavy traffic, and some of the requests have stringent QoS requirements. But then, satisfying those requests can only be done at the expense of reducing the overall system capacity and of limiting the number of users who can be served.