We　consider　a　system　of　two　separated　cavities　with　the　cavity　fields　initially　prepared　in　a　two-mode　squeezed　vacuum　state　(TMSVS).　We　investigate　the　short　time　evolution　of　Bell-nonlocality　of　the　fields　interacting　with　one　or　two　atoms.　It　is　shown　that　the　Bell-inequality　violation　of　the　fields　can　be　fully　destroyed　in　a　finite　time　and　reappears　in　the　later　time.　After　Bell-nonlocality　sudden　death　(BNSD)　in　some　cases,　Bell-nonlocality　of　the　fields　almost　but　does　not　totally　return　to　its　initial　value　when　the　squeezing　parameter　for　the　fields　is　small.　The　pattern　of　Bell-nonlocality　evolution　is　dependent　on　the　squeezing　parameter　of　the　fields,　the　detuning　between　the　atomic　transition　and　field　frequency　and　the　differences　between　atom-field　couplings.　(C)　2011　Elsevier　B.V.　All　rights　reserved.