Let {${Omega}$, $mathcal{F}$, P} be a probability space and {$X_n{mid}n{geq}1$} be a sequence of random variables defined on it. A finite sequence of random variables {$X_i{mid}1{leq}i{leq}n$} is a conditional associated given $mathcal{F}$ if for any coordinate-wise nondecreasing functions f and g defined on $R^n$, $Cov^{mathcal{F}}$ (f($X_1$, ${ldots}$, $X_n$), g($X_1$, ${ldots}$, $X_n$)) ${geq}$ 0 a.s. whenever the conditional covariance exists. We obtain the H$grave{a}$jek-R$grave{e}$nyi-type inequality for conditional associated random variables. In addition, we establish the strong law of large numbers, the three series theorem, integrability of supremum, and a strong growth rate for $mathcal{F}$-associated random variables.