Abstract: Temporal logics are typically used for the specification of real-time systems since they are capable of describing temporal constraints among events and actions: properties of invariance, precedence, periodicity, repeated occurrences, liveness and safety conditions, etc. This paper describes an evolution of the Temporal Interval Logic called TILCO. TILCO is based on time intervals and can concisely express temporal constraints with time bounds. In this paper, TILCO-X extension of TILCO is presented. TILCO-X proposes two new operators that strongly increase conciseness and readability of specifications to allow describing (i) the temporal ordering of events without distinction between past and future, and (ii) predicates depending on the number of occurrences of events in intervals. TILCO- X is capable to describe specifications by using a lower number of quantifications and of nesting levels between temporal operators. This paper also presents the semantics of TILCO-X and related examples showing the power of the model proposed in terms of conciseness.