I think a little bit more detail may help the community answer your question. Below are a few clarifying questions:
1) For the 60 respondents who might fill out the one survey, do they also need to fill out the other survey or will each respondent only complete one or the other?
2) Is it known who the 60 individuals are or should this be done randomly?
3) Should the 60 respondents know that they are completing an additional survey (if they need to complete both) or should it feel like they are completing just one survey?
Depending on the answer to the questions above, the best routes to take would be either using email distribution to send the survey to the correct individuals (if it is known who should get which survey). This could be done by creating separate contact lists and sending an email with the appropriate survey to the contact lists. https://www.qualtrics.com/support/survey-platform/distributions-module/email-distribution/emails-overview/
If the 60 should complete both surveys, this can be done through an end of survey action where you set up the additional survey the 60 need to complete and setting the end of survey action for that survey to launch the survey that everyone needs to complete...so they would flow from one survey to the next. To do this, use the redirect to a url option described here and have the URL be the address of the 2nd survey. https://www.qualtrics.com/support/survey-platform/survey-module/survey-flow/standard-elements/end-of-survey-element/#CustomizationOptions
Finally if it is random who the 60 should be, you will need to use quotas and branching. These are described in the two links below. https://www.qualtrics.com/support/survey-platform/survey-module/survey-tools/quotas/ | https://www.qualtrics.com/support/survey-platform/survey-module/survey-flow/standard-elements/branch-logic/
In summary, what you are looking to do is almost certainly possible with the built-in capabilities of Qualtrics and it will likely require a bit of experimenting to make it fit your exact business rules. Hope this helps.

sorry here a bit more information.
thanks for the info.
so i have 2 survey links. the first 60 respondents or randomly 60 respondents fill out survey 1. After that survey 1 has 60 responses, respondents should only see survey 2.
1) For the 60 respondents who might fill out the one survey, do they also need to fill out the other survey or will each respondent only complete one or the other? no they should only complete one survey
2) Is it known who the 60 individuals are or should this be done randomly? it should be done randomly, it could be the first 60 respondents or randomly but not more than 60. we don't have emails, it are people that participate online from a pool that is not known yet.
3) Should the 60 respondents know that they are completing an additional survey (if they need to complete both) or should it feel like they are completing just one survey? no, so only 60 people fill out survey 1, the rest of the participants participating should not see survey 1 but only survey 2

thanks a lot, hope i clarified enough.

I would do it through contacts lists and quotas. You can send out invitation one to a subset of invitees with a quota of 60.
Once that's reached, send out the second invite to remainder of invitees with the link to second survey.
Alternatively, you can program both surveys into one by using blocks and survey flow. And once a quota of 60 is reached, route them to the second "survey" logic.

hi
also just a question, how do you branch between surveys? i have used branching before for questions but not for surveys.
thanks a lot for the help

I used the word "surveys" loosely here. You can organize the two surveys within one by using blocks, and then organize those blocks in Survey Flow branching.
Or you can use the redirect to another survey in branch logic instead of having the questions of the second survey within the same.
Many options here. Depends on how you want to analyze results later as well.

Thanks,
Well I had initially the two surveys in one link and I had build two groups (each group consists of different blocks - blocks for survey 1 and the other group (blocks for survey 2);) see below can i then branch between the groups?

Just use quota checks in the branching logic. This support page has information on how to check for quotas in survey flow (towards the bottom of the page):
https://www.qualtrics.com/support/survey-platform/survey-module/survey-tools/quotas/#SettingAQuotaLimit

the thing is that there is no contact list . It will be taken place in a lab. would it be possible to have for instance the first 60 fill out survey 1/group1 and the rest survey 2/group2?
kind regards
elke

thanks a lot for your help!!
i will try using quotas and branching logics.