Ygthkb

Consider the following MWE:

documentclass{beamer}

usepackage[utf8]{inputenc}

usepackage[T1]{fontenc}

usepackage[ngerman]{babel}

usepackage{tikz,alphalph,amsmath}

setbeamertemplate{navigation symbols}{}

usetheme{AnnArbor}

usecolortheme{dolphin}

setbeamercolor{frametitle}{fg=structure,bg=white}

setbeamerfont{frametitle}{shape=rmbfseries}

newcommand{caesar}[1]{

    centering

    begin{tikzpicture}[every node/.style={draw,minimum width=1cm,minimum height=1cm}]

        foreach k in {1,...,26}

        {

            pgfmathsetmacrosecure{int(k+#1)}

            ifnumk=26

                pgfmathsetmacromainx{mod(k,26)}

            else

                pgfmathsetmacromainx{mod(k,26)-1}

            fi

            pgfmathsetmacroxpos{mod(mainx,5)}

            pgfmathsetmacrotestnumber{mod(k,5)}



            ifcasetestnumber=0

                pgfmathsetmacroypos{-floor(k/5)+1}

            else

                pgfmathsetmacroypos{-floor(k/5)}

            fi





            pgfmathsetmacroletter{int(mod(secure,26))}

            ifnumletter=0

                pgfmathsetmacroletter{26}

            elsefi



            node at (xpos,ypos) {strutalphalph{letter}};

        }



        node[draw=none] at (7,0) {$(x+textcolor{red}{e})mod 26$ mit $textcolor{red}{e} = #1$};

    end{tikzpicture}

}

begin{document}

    title{bf Title}

    author{Name}

    institute{Institute}

    maketitle



    begin{frame}{Cäsar-Verschlüsselung}

        only<1>{

            caesar{0}

        }

        only<2>{

            caesar{1}

        }

    end{frame}

end{document}

As you see, the position of the tikzpicture in the third frame is different from the second one (it's a little bit shifted to the right). I guess it's related a kind of the boxes, which the package alphalph uses for the letters of sth. like that.

My questions is: How can I fix this "bug" (in meaning of that there is no shifting when the third frame appears)?

The actual reason is way simpler. You included spurious spaces with the way you used only which lead to the shift. You have to make sure to comment out line endings using %:

documentclass{beamer}

usepackage[utf8]{inputenc}

usepackage[T1]{fontenc}

usepackage[ngerman]{babel}

usepackage{tikz,alphalph,amsmath}

setbeamertemplate{navigation symbols}{}

usetheme{AnnArbor}

usecolortheme{dolphin}

setbeamercolor{frametitle}{fg=structure,bg=white}

setbeamerfont{frametitle}{shape=rmbfseries}

newcommand{caesar}[1]{

    centering

    begin{tikzpicture}[every node/.style={draw,minimum width=1cm,minimum height=1cm}]

        foreach k in {1,...,26}

        {

            pgfmathsetmacrosecure{int(k+#1)}

            ifnumk=26

                pgfmathsetmacromainx{mod(k,26)}

            else

                pgfmathsetmacromainx{mod(k,26)-1}

            fi

            pgfmathsetmacroxpos{mod(mainx,5)}

            pgfmathsetmacrotestnumber{mod(k,5)}



            ifcasetestnumber=0

                pgfmathsetmacroypos{-floor(k/5)+1}

            else

                pgfmathsetmacroypos{-floor(k/5)}

            fi





            pgfmathsetmacroletter{int(mod(secure,26))}

            ifnumletter=0

                pgfmathsetmacroletter{26}

            elsefi



            node at (xpos,ypos) {strutmakebox[1em]{alphalph{letter}}};

        }



        node[draw=none] at (7,0) {$(x+textcolor{red}{e})mod 26$ mit $textcolor{red}{e} = #1$};

    end{tikzpicture}

}

begin{document}

    title{bf Title}

    author{Name}

    institute{Institute}

    maketitle



    begin{frame}{Cäsar-Verschlüsselung}

        only<1>{%

            caesar{0}%

        }%

        only<2>{%

            caesar{1}%

        }%

    end{frame}

end{document}