Monotonicity criteria are established for the generalized MarcumQ-function,QM(alpha,beta), the standard NuttallQ-function,QM,N(alpha,beta) , and the normalized NuttallQ-function,QM,N(alpha,beta), with respect to their real order indicesM,N. Besides, closed-form expressions are derived for the computation of the standard and normalized NuttallQ-functions for the case whenM,Nare odd multiples of 0.5 andMgesN. By exploiting these results, novel upper and lower bounds forQM,N(alpha,beta) andQM,N(alpha,beta) are proposed. Furthermore, specific tight upper and lower bounds forQM(alpha,beta), previously reported in the literature, are extended for real values ofM. The offered theoretical results can be efficiently applied in the study of digital communications over fading channels, in the information-theoretic analysis of multiple-input multiple-output systems and in the description of stochastic processes in probability theory, among others.