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Let f(x) = xn -- axm -- b be a monic irreducible polynomial of degree nhaving integer coefficients. Let K = Q(θ) be an algebraic number field with θ a root of f(x). In this paper, we provide some explicit conditions involving only a,b,m,n for which K is not monogenic. Further, as an application, in a special case, we show that if p is a prime number of the form 32k +1, k ∈ Z and θ is a root of a monic polynomial x32n -- 64axm -- p with 2 + n p|a Q(θ) is not monogenic. [ABSTRACT FROM AUTHOR]