1.anxious担心的，焦急的，惦记的(for或about);渴望的,(for)。
We are anxious about [ for] his safety.
我们为他的安全担忧。《汉英大词典》
She is very anxious about her dear old mother.
她十分惦念年迈的老母亲。
Parents are naturally anxious for their children.
父母自然为儿女担心。《牛津高阶英汉双解词典》
They are anxious for her safety.
他们为她的安全担心。《牛津高阶英汉双解词典》
She was anxious for me to unwrap the other gifts.
她急切地等我打开其他礼物。
He seemed anxious about the meeting.
他似乎对这次会议忧心忡忡。
She was weepy and nervy, anxious about her baby.
她动不动就哭，而且神经紧张，总为她的小宝贝担心。
I believe he is most painfully anxious about Diana.
我相信他肯定非常担心黛安娜。
We are anxious about her safety. 我们为她的安全担心。
They are anxious for peace. 他们渴望和平。
I was anxious for your help.
我渴望你的帮助。
2.eager渴望的，热切的，指对成功的热情，常同for，after 或 about连用。
He is eager for success. 他渴望成功。
They were eager for a second bite of the cherry.
他们渴望能得到第二次机会。
She is eager for her parents' approval.
她渴望得到父母的赞许。
Haig was desperately eager for an affirmative answer
黑格非常渴望得到一个肯定的回答。
He is eager about going. 他急切想去。(本句不可用for)
She is eager about her progress. 她渴望进步。
提示
1.eager 和anxious后均可接不定式，表示"急切"。
He is eager to see his parents. 他急切想见到父母。
They are anxious to know the result. 他们急切想知道结果。
2.eager和anxious后均可接that从句，表示"急切"，从句用should 型虚拟语气。
We are anxious that he(should)avoid the mistake. 我们希望他能避免出错。
The boss is eager that the workers ( should) come in time.
老板热切期望工人都能按时来。
We are eager that the project (should )be started early.
我们热切希望这项计划能早日着手进行。