1.anxious擔心的，焦急的，惦記的(for或about);渴望的,(for)。
We are anxious about [ for] his safety.
我們為他的安全擔憂。《漢英大詞典》
She is very anxious about her dear old mother.
她十分惦念年邁的老母親。
Parents are naturally anxious for their children.
父母自然為兒女擔心。《牛津高階英漢雙解詞典》
They are anxious for her safety.
他們為她的安全擔心。《牛津高階英漢雙解詞典》
She was anxious for me to unwrap the other gifts.
她急切地等我打開其他禮物。
He seemed anxious about the meeting.
他似乎對這次會議憂心忡忡。
She was weepy and nervy, anxious about her baby.
她動不動就哭，而且神經緊張，總為她的小寶貝擔心。
I believe he is most painfully anxious about Diana.
我相信他肯定非常擔心黛安娜。
We are anxious about her safety. 我們為她的安全擔心。
They are anxious for peace. 他們渴望和平。
I was anxious for your help.
我渴望你的幫助。
2.eager渴望的，熱切的，指對成功的熱情，常同for，after 或 about連用。
He is eager for success. 他渴望成功。
They were eager for a second bite of the cherry.
他們渴望能得到第二次機會。
She is eager for her parents' approval.
她渴望得到父母的贊許。
Haig was desperately eager for an affirmative answer
黑格非常渴望得到一個肯定的回答。
He is eager about going. 他急切想去。(本句不可用for)
She is eager about her progress. 她渴望進步。
提示
1.eager 和anxious後均可接不定式，表示"急切"。
He is eager to see his parents. 他急切想見到父母。
They are anxious to know the result. 他們急切想知道結果。
2.eager和anxious後均可接that從句，表示"急切"，從句用should 型虛拟語氣。
We are anxious that he(should)avoid the mistake. 我們希望他能避免出錯。
The boss is eager that the workers ( should) come in time.
老闆熱切期望勞工都能按時來。
We are eager that the project (should )be started early.
我們熱切希望這項計劃能早日着手進行。